Proofgold Address

Prim wn : ο → ο
Prim wb : ο → ο → ο
Prim wo : ο → ο → ο
Prim wa : ο → ο → ο
Prim wif : ο → ο → ο → ο
Prim w3o : ο → ο → ο → ο
Prim w3a : ο → ο → ο → ο
Prim wnan : ο → ο → ο
Prim wxo : ο → ο → ο
Prim cv : ι → ι → ο
Prim wceq^wceq : (ι → ο) → (ι → ο) → ο
Prim wtru : ο
Prim wfal : ο
Prim whad : ο → ο → ο → ο
Prim wcad : ο → ο → ο → ο
Prim wex : (ι → ο) → ο
Prim wnf : (ι → ο) → ο
Prim wnfOLD : (ι → ο) → ο
Prim wsb : (ι → ο) → ι → ο
Prim wcel : (ι → ο) → (ι → ο) → ο
Prim weu : (ι → ο) → ο
Prim wmo : (ι → ο) → ο
Prim cab : (ι → ο) → ι → ο
Prim wnfc : (ι → ι → ο) → ο
Prim wne : (ι → ο) → (ι → ο) → ο
Prim wnel : (ι → ο) → (ι → ο) → ο
Prim wral : (ι → ο) → (ι → ι → ο) → ο
Prim wrex : (ι → ο) → (ι → ι → ο) → ο
Prim wreu : (ι → ο) → (ι → ι → ο) → ο
Prim wrmo : (ι → ο) → (ι → ι → ο) → ο
Prim crab : (ι → ο) → (ι → ι → ο) → ι → ο
Prim cvv : ι → ο
Prim wcdeq : ο → ι → ι → ο
Prim wsbc^wsbc : (ι → ο) → (ι → ο) → ο
Prim csb : (ι → ο) → (ι → ι → ο) → ι → ο
Prim cdif : (ι → ο) → (ι → ο) → ι → ο
Prim cun : (ι → ο) → (ι → ο) → ι → ο
Prim cin : (ι → ο) → (ι → ο) → ι → ο
Prim wss : (ι → ο) → (ι → ο) → ο
Prim wpss : (ι → ο) → (ι → ο) → ο
Prim csymdif : (ι → ο) → (ι → ο) → ι → ο
Prim c0 : ι → ο
Prim cif : ο → (ι → ο) → (ι → ο) → ι → ο
Prim cpw : (ι → ο) → ι → ο
Prim csn : (ι → ο) → ι → ο
Prim cpr : (ι → ο) → (ι → ο) → ι → ο
Prim ctp : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cop : (ι → ο) → (ι → ο) → ι → ο
Prim cotp : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cuni : (ι → ο) → ι → ο
Prim cint : (ι → ο) → ι → ο
Prim ciun : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim ciin : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim wdisj : (ι → ι → ο) → (ι → ι → ο) → ο
Prim wbr : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim copab : (ι → ι → ο) → ι → ο
Prim copab_b : (ι → ο) → ι → ο
Prim cmpt : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim wtr : (ι → ο) → ο
Prim cid : ι → ο
Prim cep : ι → ο
Prim wpo : (ι → ο) → (ι → ο) → ο
Prim wor : (ι → ο) → (ι → ο) → ο
Prim wfr : (ι → ο) → (ι → ο) → ο
Prim wse : (ι → ο) → (ι → ο) → ο
Prim wwe : (ι → ο) → (ι → ο) → ο
Prim cxp : (ι → ο) → (ι → ο) → ι → ο
Prim ccnv : (ι → ο) → ι → ο
Prim cdm : (ι → ο) → ι → ο
Prim crn : (ι → ο) → ι → ο
Prim cres : (ι → ο) → (ι → ο) → ι → ο
Prim cima : (ι → ο) → (ι → ο) → ι → ο
Prim ccom : (ι → ο) → (ι → ο) → ι → ο
Prim wrel : (ι → ο) → ο
Prim cpred : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim word : (ι → ο) → ο
Prim con0 : ι → ο
Prim wlim : (ι → ο) → ο
Prim csuc : (ι → ο) → ι → ο
Prim cio : (ι → ο) → ι → ο
Prim wfun : (ι → ο) → ο
Prim wfn : (ι → ο) → (ι → ο) → ο
Prim wf : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim wf1 : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim wfo : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim wf1o : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim cfv : (ι → ο) → (ι → ο) → ι → ο
Prim wiso : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim crio : (ι → ο) → (ι → ι → ο) → ι → ο
Prim co : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim coprab : (ι → ι → ι → ο) → ι → ο
Prim cmpt2 : (ι → ι → ι → ο) → (ι → ι → ι → ο) → (ι → ι → ι → ο) → ι → ο
Prim cof : (ι → ο) → ι → ο
Prim cofr : (ι → ο) → ι → ο
Prim crpss : ι → ο
Prim com : ι → ο
Prim c1st : ι → ο
Prim c2nd : ι → ο
Prim csupp : ι → ο
Prim ctpos : (ι → ο) → ι → ο
Prim ccur : (ι → ο) → ι → ο
Prim cunc : (ι → ο) → ι → ο
Prim cund : ι → ο
Prim cwrecs : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim wsmo : (ι → ο) → ο
Prim crecs : (ι → ο) → ι → ο
Prim crdg : (ι → ο) → (ι → ο) → ι → ο
Prim cseqom : (ι → ο) → (ι → ο) → ι → ο
Prim c1o : ι → ο
Prim c2o : ι → ο
Prim c3o : ι → ο
Prim c4o : ι → ο
Prim coa : ι → ο
Prim comu : ι → ο
Prim coe : ι → ο
Prim wer : (ι → ο) → (ι → ο) → ο
Prim cec : (ι → ο) → (ι → ο) → ι → ο
Prim cqs : (ι → ο) → (ι → ο) → ι → ο
Prim cmap : ι → ο
Prim cpm : ι → ο
Prim cixp : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim cen : ι → ο
Prim cdom : ι → ο
Prim csdm : ι → ο
Prim cfn : ι → ο
Prim cfsupp : ι → ο
Prim cfi : ι → ο
Prim csup : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cinf : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim coi : (ι → ο) → (ι → ο) → ι → ο
Prim char : ι → ο
Prim cwdom : ι → ο
Prim ccnf : ι → ο
Prim ctc : ι → ο
Prim cr1 : ι → ο
Prim crnk : ι → ο
Prim ccrd : ι → ο
Prim cale : ι → ο
Prim ccf : ι → ο
Prim wacn : (ι → ο) → ι → ο
Prim wac : ο
Prim ccda : ι → ο
Prim cfin1a : ι → ο
Prim cfin2 : ι → ο
Prim cfin4 : ι → ο
Prim cfin3 : ι → ο
Prim cfin5 : ι → ο
Prim cfin6 : ι → ο
Prim cfin7 : ι → ο
Prim cgch : ι → ο
Prim cwina : ι → ο
Prim cina : ι → ο
Prim cwun : ι → ο
Prim cwunm : ι → ο
Prim ctsk : ι → ο
Prim cgru : ι → ο
Prim ctskm : ι → ο
Prim cnpi : ι → ο
Prim cpli : ι → ο
Prim cmi : ι → ο
Prim clti : ι → ο
Prim cplpq : ι → ο
Prim cmpq : ι → ο
Prim cltpq : ι → ο
Prim ceq : ι → ο
Prim cnq : ι → ο
Prim c1q : ι → ο
Prim cerq : ι → ο
Prim cplq : ι → ο
Prim cmq : ι → ο
Prim crq : ι → ο
Prim cltq : ι → ο
Prim cnp : ι → ο
Prim c1p : ι → ο
Prim cpp : ι → ο
Prim cmp : ι → ο
Prim cltp : ι → ο
Prim cer : ι → ο
Prim cnr : ι → ο
Prim c0r : ι → ο
Prim c1r : ι → ο
Prim cm1r : ι → ο
Prim cplr : ι → ο
Prim cmr : ι → ο
Prim cltr : ι → ο
Prim cc : ι → ο
Prim cr : ι → ο
Prim cc0 : ι → ο
Prim c1 : ι → ο
Prim ci : ι → ο
Prim caddc : ι → ο
Prim cltrr : ι → ο
Prim cmul : ι → ο
Prim cpnf : ι → ο
Prim cmnf : ι → ο
Prim cxr : ι → ο
Prim clt : ι → ο
Prim cle : ι → ο
Prim cmin : ι → ο
Prim cneg : (ι → ο) → ι → ο
Prim cdiv : ι → ο
Prim cn : ι → ο
Prim c2 : ι → ο
Prim c3 : ι → ο
Prim c4 : ι → ο
Prim c5 : ι → ο
Prim c6 : ι → ο
Prim c7 : ι → ο
Prim c8 : ι → ο
Prim c9 : ι → ο
Prim c10 : ι → ο
Prim cn0 : ι → ο
Prim cxnn0 : ι → ο
Prim cz : ι → ο
Prim cdc : (ι → ο) → (ι → ο) → ι → ο
Prim cuz : ι → ο
Prim cq : ι → ο
Prim crp : ι → ο
Prim cxne : (ι → ο) → ι → ο
Prim cxad : ι → ο
Prim cxmu : ι → ο
Prim cioo : ι → ο
Prim cioc : ι → ο
Prim cico : ι → ο
Prim cicc : ι → ο
Prim cfz : ι → ο
Prim cfzo : ι → ο
Prim cfl : ι → ο
Prim cceil : ι → ο
Prim cmo : ι → ο
Prim cseq : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cexp : ι → ο
Prim cfa : ι → ο
Prim cbc : ι → ο
Prim chash : ι → ο
Prim cword : (ι → ο) → ι → ο
Prim clsw : ι → ο
Prim cconcat : ι → ο
Prim cs1 : (ι → ο) → ι → ο
Prim csubstr : ι → ο
Prim csplice : ι → ο
Prim creverse : ι → ο
Prim creps : ι → ο
Prim ccsh : ι → ο
Prim cs2 : (ι → ο) → (ι → ο) → ι → ο
Prim cs3 : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cs4 : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cs5 : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cs6 : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cs7 : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cs8 : (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim ctcl : ι → ο
Prim crtcl : ι → ο
Prim crelexp : ι → ο
Prim crtrcl : ι → ο
Prim cshi : ι → ο
Prim csgn : ι → ο
Prim ccj : ι → ο
Prim cre : ι → ο
Prim cim : ι → ο
Prim csqrt : ι → ο
Prim cabs : ι → ο
Prim clsp : ι → ο
Prim cli : ι → ο
Prim crli : ι → ο
Prim co1 : ι → ο
Prim clo1 : ι → ο
Prim csu : (ι → ο) → (ι → ι → ο) → ι → ο
Prim cprod : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim cfallfac : ι → ο
Prim crisefac : ι → ο
Prim cbp : ι → ο
Prim ce : ι → ο
Prim ceu : ι → ο
Prim csin : ι → ο
Prim ccos : ι → ο
Prim ctan : ι → ο
Prim cpi : ι → ο
Prim cdvds : ι → ο
Prim cbits : ι → ο
Prim csad : ι → ο
Prim csmu : ι → ο
Prim cgcd : ι → ο
Prim clcm : ι → ο
Prim clcmf : ι → ο
Prim cprime : ι → ο
Prim cnumer : ι → ο
Prim cdenom : ι → ο
Prim codz : ι → ο
Prim cphi : ι → ο
Prim cpc : ι → ο
Prim cgz : ι → ο
Prim cvdwa : ι → ο
Prim cvdwm : ι → ο
Prim cvdwp : ι → ο
Prim cram : ι → ο
Prim cprmo : ι → ο
Prim cstr : ι → ο
Prim cnx : ι → ο
Prim csts : ι → ο
Prim cslot : (ι → ο) → ι → ο
Prim cbs : ι → ο
Prim cress : ι → ο
Prim cplusg : ι → ο
Prim cmulr : ι → ο
Prim cstv : ι → ο
Prim csca : ι → ο
Prim cvsca : ι → ο
Prim cip : ι → ο
Prim cts : ι → ο
Prim cple : ι → ο
Prim coc : ι → ο
Prim cds : ι → ο
Prim cunif : ι → ο
Prim chom : ι → ο
Prim cco : ι → ο
Prim crest : ι → ο
Prim ctopn : ι → ο
Prim ctg : ι → ο
Prim cpt : ι → ο
Prim c0g : ι → ο
Prim cgsu : ι → ο
Prim cprds : ι → ο
Prim cpws : ι → ο
Prim cordt : ι → ο
Prim cxrs : ι → ο
Prim cqtop : ι → ο
Prim cimas : ι → ο
Prim cqus : ι → ο
Prim cxps : ι → ο
Prim cmre : ι → ο
Prim cmrc : ι → ο
Prim cmri : ι → ο
Prim cacs : ι → ο
Prim ccat : ι → ο
Prim ccid : ι → ο
Prim chomf : ι → ο
Prim ccomf : ι → ο
Prim coppc : ι → ο
Prim cmon : ι → ο
Prim cepi : ι → ο
Prim csect : ι → ο
Prim cinv : ι → ο
Prim ciso : ι → ο
Prim ccic : ι → ο
Prim cssc : ι → ο
Prim cresc : ι → ο
Prim csubc : ι → ο
Prim cfunc : ι → ο
Prim cidfu : ι → ο
Prim ccofu : ι → ο
Prim cresf : ι → ο
Prim cful : ι → ο
Prim cfth : ι → ο
Prim cnat : ι → ο
Prim cfuc : ι → ο
Prim cinito : ι → ο
Prim ctermo : ι → ο
Prim czeroo : ι → ο
Prim cdoma : ι → ο
Prim ccoda : ι → ο
Prim carw : ι → ο
Prim choma : ι → ο
Prim cida : ι → ο
Prim ccoa : ι → ο
Prim csetc : ι → ο
Prim ccatc : ι → ο
Prim cestrc : ι → ο
Prim cxpc : ι → ο
Prim c1stf : ι → ο
Prim c2ndf : ι → ο
Prim cprf : ι → ο
Prim cevlf : ι → ο
Prim ccurf : ι → ο
Prim cuncf : ι → ο
Prim cdiag : ι → ο
Prim chof : ι → ο
Prim cyon : ι → ο
Prim cpreset : ι → ο
Prim cdrs : ι → ο
Prim cpo : ι → ο
Prim cplt : ι → ο
Prim club : ι → ο
Prim cglb : ι → ο
Prim cjn : ι → ο
Prim cmee : ι → ο
Prim ctos : ι → ο
Prim cp0 : ι → ο
Prim cp1 : ι → ο
Prim clat : ι → ο
Prim ccla : ι → ο
Prim codu : ι → ο
Prim cipo : ι → ο
Prim cdlat : ι → ο
Prim cps : ι → ο
Prim ctsr : ι → ο
Prim cdir : ι → ο
Prim ctail : ι → ο
Prim cplusf : ι → ο
Prim cmgm : ι → ο
Prim csgrp : ι → ο
Prim cmnd : ι → ο
Prim cmhm : ι → ο
Prim csubmnd : ι → ο
Prim cfrmd : ι → ο
Prim cvrmd : ι → ο
Prim cgrp : ι → ο
Prim cminusg : ι → ο
Prim csg : ι → ο
Prim cmg : ι → ο
Prim csubg : ι → ο
Prim cnsg : ι → ο
Prim cqg : ι → ο
Prim cghm : ι → ο
Prim cgim : ι → ο
Prim cgic : ι → ο
Prim cga : ι → ο
Prim ccntz : ι → ο
Prim ccntr : ι → ο
Prim coppg : ι → ο
Prim csymg : ι → ο
Prim cpmtr : ι → ο
Prim cpsgn : ι → ο
Prim cevpm : ι → ο
Prim cod : ι → ο
Prim cgex : ι → ο
Prim cpgp : ι → ο
Prim cslw : ι → ο
Prim clsm : ι → ο
Prim cpj1 : ι → ο
Prim cefg : ι → ο
Prim cfrgp : ι → ο
Prim cvrgp : ι → ο
Prim ccmn : ι → ο
Prim cabl : ι → ο
Prim ccyg : ι → ο
Prim cdprd : ι → ο
Prim cdpj : ι → ο
Prim cmgp : ι → ο
Prim cur : ι → ο
Prim csrg : ι → ο
Prim crg : ι → ο
Prim ccrg : ι → ο
Prim coppr : ι → ο
Prim cdsr : ι → ο
Prim cui : ι → ο
Prim cir : ι → ο
Prim cinvr : ι → ο
Prim cdvr : ι → ο
Prim crpm : ι → ο
Prim crh : ι → ο
Prim crs : ι → ο
Prim cric : ι → ο
Prim cdr : ι → ο
Prim cfield : ι → ο
Prim csubrg : ι → ο
Prim crgspn : ι → ο
Prim cabv : ι → ο
Prim cstf : ι → ο
Prim csr : ι → ο
Prim clmod : ι → ο
Prim cscaf : ι → ο
Prim clss : ι → ο
Prim clspn : ι → ο
Prim clmhm : ι → ο
Prim clmim : ι → ο
Prim clmic : ι → ο
Prim clbs : ι → ο
Prim clvec : ι → ο
Prim csra : ι → ο
Prim crglmod : ι → ο
Prim clidl : ι → ο
Prim crsp : ι → ο
Prim c2idl : ι → ο
Prim clpidl : ι → ο
Prim clpir : ι → ο
Prim cnzr : ι → ο
Prim crlreg : ι → ο
Prim cdomn : ι → ο
Prim cidom : ι → ο
Prim cpid : ι → ο
Prim casa : ι → ο
Prim casp : ι → ο
Prim cascl : ι → ο
Prim cmps : ι → ο
Prim cmvr : ι → ο
Prim cmpl : ι → ο
Prim cltb : ι → ο
Prim copws : ι → ο
Prim ces : ι → ο
Prim cevl : ι → ο
Prim cmhp : ι → ο
Prim cpsd : ι → ο
Prim cslv : ι → ο
Prim cai : ι → ο
Prim cps1 : ι → ο
Prim cv1 : ι → ο
Prim cpl1 : ι → ο
Prim cco1 : ι → ο
Prim ctp1 : ι → ο
Prim ces1 : ι → ο
Prim ce1 : ι → ο
Prim cpsmet : ι → ο
Prim cxmt : ι → ο
Prim cme : ι → ο
Prim cbl : ι → ο
Prim cfbas : ι → ο
Prim cfg : ι → ο
Prim cmopn : ι → ο
Prim cmetu : ι → ο
Prim ccnfld : ι → ο
Prim zring : ι → ο
Prim czrh : ι → ο
Prim czlm : ι → ο
Prim cchr : ι → ο
Prim czn : ι → ο
Prim crefld : ι → ο
Prim cphl : ι → ο
Prim cipf : ι → ο
Prim cocv : ι → ο
Prim ccss : ι → ο
Prim cthl : ι → ο
Prim cpj : ι → ο
Prim chs : ι → ο
Prim cobs : ι → ο
Prim cdsmm : ι → ο
Prim cfrlm : ι → ο
Prim cuvc : ι → ο
Prim clindf : ι → ο
Prim clinds : ι → ο
Prim cmmul : ι → ο
Prim cmat : ι → ο
Prim cdmat : ι → ο
Prim cscmat : ι → ο
Prim cmvmul : ι → ο
Prim cmarrep : ι → ο
Prim cmatrepV : ι → ο
Prim csubma : ι → ο
Prim cmdat : ι → ο
Prim cmadu : ι → ο
Prim cminmar1 : ι → ο
Prim ccpmat : ι → ο
Prim cmat2pmat : ι → ο
Prim ccpmat2mat : ι → ο
Prim cdecpmat : ι → ο
Prim cpm2mp : ι → ο
Prim cchpmat : ι → ο
Prim ctop : ι → ο
Prim ctopon : ι → ο
Prim ctps : ι → ο
Prim ctb : ι → ο
Prim ccld : ι → ο
Prim cnt : ι → ο
Prim ccl : ι → ο
Prim cnei : ι → ο
Prim clp : ι → ο
Prim cperf : ι → ο
Prim ccn : ι → ο
Prim ccnp : ι → ο
Prim clm : ι → ο
Prim ct0 : ι → ο
Prim ct1 : ι → ο
Prim cha : ι → ο
Prim creg : ι → ο
Prim cnrm : ι → ο
Prim ccnrm : ι → ο
Prim cpnrm : ι → ο
Prim ccmp : ι → ο
Prim cconn : ι → ο
Prim c1stc : ι → ο
Prim c2ndc : ι → ο
Prim clly : (ι → ο) → ι → ο
Prim cnlly : (ι → ο) → ι → ο
Prim cref : ι → ο
Prim cptfin : ι → ο
Prim clocfin : ι → ο
Prim ckgen : ι → ο
Prim ctx : ι → ο
Prim cxko : ι → ο
Prim ckq : ι → ο
Prim chmeo : ι → ο
Prim chmph : ι → ο
Prim cfil : ι → ο
Prim cufil : ι → ο
Prim cufl : ι → ο
Prim cfm : ι → ο
Prim cflim : ι → ο
Prim cflf : ι → ο
Prim cfcls : ι → ο
Prim cfcf : ι → ο
Prim ccnext : ι → ο
Prim ctmd : ι → ο
Prim ctgp : ι → ο
Prim ctsu : ι → ο
Prim ctrg : ι → ο
Prim ctdrg : ι → ο
Prim ctlm : ι → ο
Prim ctvc : ι → ο
Prim cust : ι → ο
Prim cutop : ι → ο
Prim cuss : ι → ο
Prim cusp : ι → ο
Prim ctus : ι → ο
Prim cucn : ι → ο
Prim ccfilu : ι → ο
Prim ccusp : ι → ο
Prim cxme : ι → ο
Prim cmt : ι → ο
Prim ctmt : ι → ο
Prim cnm : ι → ο
Prim cngp : ι → ο
Prim ctng : ι → ο
Prim cnrg : ι → ο
Prim cnlm : ι → ο
Prim cnvc : ι → ο
Prim cnmo : ι → ο
Prim cnghm : ι → ο
Prim cnmhm : ι → ο
Prim cii : ι → ο
Prim ccncf : ι → ο
Prim chtpy : ι → ο
Prim cphtpy : ι → ο
Prim cphtpc : ι → ο
Prim cpco : ι → ο
Prim comi : ι → ο
Prim comn : ι → ο
Prim cpi1 : ι → ο
Prim cpin : ι → ο
Prim cclm : ι → ο
Prim ccvs : ι → ο
Prim ccph : ι → ο
Prim ctch : ι → ο
Prim ccfil : ι → ο
Prim cca : ι → ο
Prim cms : ι → ο
Prim ccms : ι → ο
Prim cbn : ι → ο
Prim chl : ι → ο
Prim crrx : ι → ο
Prim cehl : ι → ο
Prim covol : ι → ο
Prim cvol : ι → ο
Prim cmbf : ι → ο
Prim citg1 : ι → ο
Prim citg2 : ι → ο
Prim cibl : ι → ο
Prim citg : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim c0p : ι → ο
Prim cdit : (ι → ι → ο) → (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim climc : ι → ο
Prim cdv : ι → ο
Prim cdvn : ι → ο
Prim ccpn : ι → ο
Prim cmdg : ι → ο
Prim cdg1 : ι → ο
Prim cmn1 : ι → ο
Prim cuc1p : ι → ο
Prim cq1p : ι → ο
Prim cr1p : ι → ο
Prim cig1p : ι → ο
Prim cply : ι → ο
Prim cidp : ι → ο
Prim ccoe : ι → ο
Prim cdgr : ι → ο
Prim cquot : ι → ο
Prim caa : ι → ο
Prim ctayl : ι → ο
Prim cana : ι → ο
Prim culm : ι → ο
Prim clog : ι → ο
Prim ccxp : ι → ο
Prim clogb : ι → ο
Prim casin : ι → ο
Prim cacos : ι → ο
Prim catan : ι → ο
Prim carea : ι → ο
Prim cem : ι → ο
Prim czeta : ι → ο
Prim clgam : ι → ο
Prim cgam : ι → ο
Prim cigam : ι → ο
Prim ccht : ι → ο
Prim cvma : ι → ο
Prim cchp : ι → ο
Prim cppi : ι → ο
Prim cmu : ι → ο
Prim csgm : ι → ο
Prim cdchr : ι → ο
Prim clgs : ι → ο
Prim cstrkg : ι → ο
Prim cstrkgc : ι → ο
Prim cstrkgb : ι → ο
Prim cstrkgcb : ι → ο
Prim cstrkgld : ι → ο
Prim cstrkge : ι → ο
Prim citv : ι → ο
Prim clng : ι → ο
Prim ccgrg : ι → ο
Prim cismt : ι → ο
Prim cleg : ι → ο
Prim chlg : ι → ο
Prim cmir : ι → ο
Prim crag : ι → ο
Prim cperpg : ι → ο
Prim chpg : ι → ο
Prim cmid : ι → ο
Prim clmi : ι → ο
Prim ccgra : ι → ο
Prim cinag : ι → ο
Prim cleag : ι → ο
Prim ceqlg : ι → ο
Prim cttg : ι → ο
Prim cee : ι → ο
Prim cbtwn : ι → ο
Prim ccgr : ι → ο
Prim ceeng : ι → ο
Prim cedgf : ι → ο
Prim cvtx : ι → ο
Prim ciedg : ι → ο
Prim cedg : ι → ο
Prim cuhgr : ι → ο
Prim cushgr : ι → ο
Prim cupgr : ι → ο
Prim cumgr : ι → ο
Prim cuspgr : ι → ο
Prim cusgr : ι → ο
Prim csubgr : ι → ο
Prim cfusgr : ι → ο
Prim cnbgr : ι → ο
Prim cuvtx : ι → ο
Prim ccplgr : ι → ο
Prim ccusgr : ι → ο
Prim cvtxdg : ι → ο
Prim crgr : ι → ο
Prim crusgr : ι → ο
Prim cewlks : ι → ο
Prim cwlks : ι → ο
Prim cwlkson : ι → ο
Prim ctrls : ι → ο
Prim ctrlson : ι → ο
Prim cpths : ι → ο
Prim cspths : ι → ο
Prim cpthson : ι → ο
Prim cspthson : ι → ο
Prim cclwlks : ι → ο
Prim ccrcts : ι → ο
Prim ccycls : ι → ο
Prim cwwlks : ι → ο
Prim cwwlksn : ι → ο
Prim cwwlksnon : ι → ο
Prim cwwspthsn : ι → ο
Prim cwwspthsnon : ι → ο
Prim cclwwlk : ι → ο
Prim cclwwlkn : ι → ο
Prim cclwwlknold : ι → ο
Prim cclwwlknon : ι → ο
Prim cconngr : ι → ο
Prim ceupth : ι → ο
Prim cfrgr : ι → ο
Prim cplig : ι → ο
Prim cgr : ι → ο
Prim cgi : ι → ο
Prim cgn : ι → ο
Prim cgs : ι → ο
Prim cablo : ι → ο
Prim cvc : ι → ο
Prim cnv : ι → ο
Prim cpv : ι → ο
Prim cba : ι → ο
Prim cns : ι → ο
Prim cn0v : ι → ο
Prim cnsb : ι → ο
Prim cnmcv : ι → ο
Prim cims : ι → ο
Prim cdip : ι → ο
Prim css : ι → ο
Prim clno : ι → ο
Prim cnmoo : ι → ο
Prim cblo : ι → ο
Prim c0o : ι → ο
Prim caj : ι → ο
Prim chmo : ι → ο
Prim ccphlo : ι → ο
Prim ccbn : ι → ο
Prim chlo : ι → ο
Prim chil : ι → ο
Prim cva : ι → ο
Prim csm : ι → ο
Prim csp : ι → ο
Prim cno : ι → ο
Prim c0v : ι → ο
Prim cmv : ι → ο
Prim ccau : ι → ο
Prim chli : ι → ο
Prim csh : ι → ο
Prim cch : ι → ο
Prim cort : ι → ο
Prim cph : ι → ο
Prim cspn : ι → ο
Prim chj : ι → ο
Prim chsup : ι → ο
Prim c0h : ι → ο
Prim ccm : ι → ο
Prim cpjh : ι → ο
Prim chos : ι → ο
Prim chot : ι → ο
Prim chod : ι → ο
Prim chfs : ι → ο
Prim chft : ι → ο
Prim ch0o : ι → ο
Prim chio : ι → ο
Prim cnop : ι → ο
Prim ccop : ι → ο
Prim clo : ι → ο
Prim cbo : ι → ο
Prim cuo : ι → ο
Prim cho : ι → ο
Prim cnmf : ι → ο
Prim cnl : ι → ο
Prim ccnfn : ι → ο
Prim clf : ι → ο
Prim cado : ι → ο
Prim cbr : ι → ο
Prim ck : ι → ο
Prim cleo : ι → ο
Prim cei : ι → ο
Prim cel : ι → ο
Prim cspc : ι → ο
Prim cst : ι → ο
Prim chst : ι → ο
Prim ccv : ι → ο
Prim cat : ι → ο
Prim cmd : ι → ο
Prim cdmd : ι → ο
Prim cdp2 : (ι → ο) → (ι → ο) → ι → ο
Prim cdp : ι → ο
Prim cxdiv : ι → ο
Prim comnd : ι → ο
Prim cogrp : ι → ο
Prim csgns : ι → ο
Prim cinftm : ι → ο
Prim carchi : ι → ο
Prim cslmd : ι → ο
Prim corng : ι → ο
Prim cofld : ι → ο
Prim cresv : ι → ο
Prim csmat : ι → ο
Prim clmat : ι → ο
Prim ccref : (ι → ο) → ι → ο
Prim cldlf : ι → ο
Prim cpcmp : ι → ο
Prim cmetid : ι → ο
Prim cpstm : ι → ο
Prim chcmp : ι → ο
Prim cqqh : ι → ο
Prim crrh : ι → ο
Prim crrext : ι → ο
Prim cxrh : ι → ο
Prim cmntop : ι → ο
Prim cind : ι → ο
Prim cesum : (ι → ι → ο) → (ι → ι → ο) → ι → ο
Prim cofc : (ι → ο) → ι → ο
Prim csiga : ι → ο
Prim csigagen : ι → ο
Prim cbrsiga : ι → ο
Prim csx : ι → ο
Prim cmeas : ι → ο
Prim cdde : ι → ο
Prim cae : ι → ο
Prim cfae : ι → ο
Prim cmbfm : ι → ο
Prim coms : ι → ο
Prim ccarsg : ι → ο
Prim citgm : ι → ο
Prim csitm : ι → ο
Prim csitg : ι → ο
Prim csseq : ι → ο
Prim cfib : ι → ο
Prim cprb : ι → ο
Prim ccprob : ι → ο
Prim crrv : ι → ο
Prim corvc : (ι → ο) → ι → ο
Prim crepr : ι → ο
Prim cvts : ι → ο
Prim cstrkg2d : ι → ο
Prim cafs : ι → ο
Prim w_bnj17 : ο → ο → ο → ο → ο
Prim c_bnj14 : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim w_bnj13 : (ι → ο) → (ι → ο) → ο
Prim w_bnj15 : (ι → ο) → (ι → ο) → ο
Prim c_bnj18 : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim w_bnj19 : (ι → ο) → (ι → ο) → (ι → ο) → ο
Prim cretr : ι → ο
Prim cpconn : ι → ο
Prim csconn : ι → ο
Prim ccvm : ι → ο
Prim cgoe : ι → ο
Prim cgna : ι → ο
Prim cgol : (ι → ο) → (ι → ο) → ι → ο
Prim csat : ι → ο
Prim cfmla : ι → ο
Prim csate : ι → ο
Prim cprv : ι → ο
Prim cgon : (ι → ο) → ι → ο
Prim cgoa : ι → ο
Prim cgoi : ι → ο
Prim cgoo : ι → ο
Prim cgob : ι → ο
Prim cgoq : ι → ο
Prim cgox : (ι → ο) → (ι → ο) → ι → ο
Prim cgze : ι → ο
Prim cgzr : ι → ο
Prim cgzp : ι → ο
Prim cgzu : ι → ο
Prim cgzg : ι → ο
Prim cgzi : ι → ο
Prim cgzf : ι → ο
Prim cmcn : ι → ο
Prim cmvar : ι → ο
Prim cmty : ι → ο
Prim cmvt : ι → ο
Prim cmtc : ι → ο
Prim cmax : ι → ο
Prim cmrex : ι → ο
Prim cmex : ι → ο
Prim cmdv : ι → ο
Prim cmvrs : ι → ο
Prim cmrsub : ι → ο
Prim cmsub : ι → ο
Prim cmvh : ι → ο
Prim cmpst : ι → ο
Prim cmsr : ι → ο
Prim cmsta : ι → ο
Prim cmfs : ι → ο
Prim cmcls : ι → ο
Prim cmpps : ι → ο
Prim cmthm : ι → ο
Prim cm0s : ι → ο
Prim cmsa : ι → ο
Prim cmwgfs : ι → ο
Prim cmsy : ι → ο
Prim cmesy : ι → ο
Prim cmgfs : ι → ο
Prim cmtree : ι → ο
Prim cmst : ι → ο
Prim cmsax : ι → ο
Prim cmufs : ι → ο
Prim cmuv : ι → ο
Prim cmvl : ι → ο
Prim cmvsb : ι → ο
Prim cmfsh : ι → ο
Prim cmfr : ι → ο
Prim cmevl : ι → ο
Prim cmdl : ι → ο
Prim cusyn : ι → ο
Prim cgmdl : ι → ο
Prim cmitp : ι → ο
Prim cmfitp : ι → ο
Prim citr : ι → ο
Prim ccpms : ι → ο
Prim chlb : ι → ο
Prim chlim : ι → ο
Prim cpfl : ι → ο
Prim csf1 : ι → ο
Prim csf : ι → ο
Prim cpsl : ι → ο
Prim czr : ι → ο
Prim cgf : ι → ο
Prim cgfo : ι → ο
Prim ceqp : ι → ο
Prim crqp : ι → ο
Prim cqp : ι → ο
Prim cqpOLD : ι → ο
Prim czp : ι → ο
Prim cqpa : ι → ο
Prim ccp : ι → ο
Prim ctrpred : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cwsuc : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cwlim : (ι → ο) → (ι → ο) → ι → ο
Prim cfrecs : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim csur : ι → ο
Prim cslt : ι → ο
Prim cbday : ι → ο
Prim csle : ι → ο
Prim csslt : ι → ο
Prim cscut : ι → ο
Prim cmade : ι → ο
Prim cold : ι → ο
Prim cnew : ι → ο
Prim cleft : ι → ο
Prim cright : ι → ο
Prim ctxp : (ι → ο) → (ι → ο) → ι → ο
Prim cpprod : (ι → ο) → (ι → ο) → ι → ο
Prim csset : ι → ο
Prim ctrans : ι → ο
Prim cbigcup : ι → ο
Prim cfix : (ι → ο) → ι → ο
Prim climits : ι → ο
Prim cfuns : ι → ο
Prim csingle : ι → ο
Prim csingles : ι → ο
Prim cimage : (ι → ο) → ι → ο
Prim ccart : ι → ο
Prim cimg : ι → ο
Prim cdomain : ι → ο
Prim crange : ι → ο
Prim capply : ι → ο
Prim ccup : ι → ο
Prim ccap : ι → ο
Prim csuccf : ι → ο
Prim cfunpart : (ι → ο) → ι → ο
Prim cfullfn : (ι → ο) → ι → ο
Prim crestrict : ι → ο
Prim cub : (ι → ο) → ι → ο
Prim clb : (ι → ο) → ι → ο
Prim caltop : (ι → ο) → (ι → ο) → ι → ο
Prim caltxp : (ι → ο) → (ι → ο) → ι → ο
Prim cofs : ι → ο
Prim ctransport : ι → ο
Prim cifs : ι → ο
Prim ccgr3 : ι → ο
Prim ccolin : ι → ο
Prim cfs : ι → ο
Prim csegle : ι → ο
Prim coutsideof : ι → ο
Prim cline2 : ι → ο
Prim cray : ι → ο
Prim clines2 : ι → ο
Prim cfwddif : ι → ο
Prim cfwddifn : ι → ο
Prim chf : ι → ο
Prim cfne : ι → ο
Prim w3nand : ο → ο → ο → ο
Prim cgcdOLD : (ι → ο) → (ι → ο) → ι → ο
Prim cprvb : ο → ο
Prim wssb : (ι → ο) → ι → ο
Prim wrnf : (ι → ο) → (ι → ι → ο) → ο
Prim bj_csngl : (ι → ο) → ι → ο
Prim bj_ctag : (ι → ο) → ι → ο
Prim bj_cproj : (ι → ο) → (ι → ο) → ι → ο
Prim bj_c1upl : (ι → ο) → ι → ο
Prim bj_cpr1 : (ι → ο) → ι → ο
Prim bj_c2uple : (ι → ο) → (ι → ο) → ι → ο
Prim bj_cpr2 : (ι → ο) → ι → ο
Prim celwise : ι → ο
Prim cmoore : ι → ο
Prim cmpt3 : (ι → ι → ι → ι → ο) → (ι → ι → ι → ι → ο) → (ι → ι → ι → ι → ο) → (ι → ι → ι → ι → ο) → ι → ο
Prim csethom : ι → ο
Prim ctophom : ι → ο
Prim cmgmhom : ι → ο
Prim ctopmgmhom : ι → ο
Prim ccur_ : ι → ο
Prim cunc_ : ι → ο
Prim cstrset : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cdiag2 : ι → ο
Prim cinftyexpi : ι → ο
Prim cccinfty : ι → ο
Prim cccbar : ι → ο
Prim cpinfty : ι → ο
Prim cminfty : ι → ο
Prim crrbar : ι → ο
Prim cinfty : ι → ο
Prim ccchat : ι → ο
Prim crrhat : ι → ο
Prim caddcc : ι → ο
Prim coppcc : ι → ο
Prim cprcpal : ι → ο
Prim carg : ι → ο
Prim cmulc : ι → ο
Prim cinvc : ι → ο
Prim cfinsum : ι → ο
Prim crrvec : ι → ο
Prim ctau : ι → ο
Prim cfinxp : (ι → ο) → (ι → ο) → ι → ο
Prim wcel_wl : (ι → ι → ο) → ο
Prim wcel2_wl : (ι → ι → ο) → ο
Prim ctotbnd : ι → ο
Prim cbnd : ι → ο
Prim cismty : ι → ο
Prim crrn : ι → ο
Prim cass : ι → ο
Prim cexid : ι → ο
Prim cmagm : ι → ο
Prim csem : ι → ο
Prim cmndo : ι → ο
Prim cghomOLD : ι → ο
Prim crngo : ι → ο
Prim cdrng : ι → ο
Prim crnghom : ι → ο
Prim crngiso : ι → ο
Prim crisc : ι → ο
Prim ccm2 : ι → ο
Prim cfld : ι → ο
Prim ccring : ι → ο
Prim cidl : ι → ο
Prim cpridl : ι → ο
Prim cmaxidl : ι → ο
Prim cprrng : ι → ο
Prim cdmn : ι → ο
Prim cigen : ι → ο
Prim cxrn : (ι → ο) → (ι → ο) → ι → ο
Prim ccoss : (ι → ο) → ι → ο
Prim ccoels : (ι → ο) → ι → ο
Prim crels : ι → ο
Prim cssr : ι → ο
Prim crefs : ι → ο
Prim crefrels : ι → ο
Prim wrefrel : (ι → ο) → ο
Prim ccnvrefs : ι → ο
Prim ccnvrefrels : ι → ο
Prim wcnvrefrel : (ι → ο) → ο
Prim csyms : ι → ο
Prim csymrels : ι → ο
Prim wsymrel : (ι → ο) → ο
Prim wprt : (ι → ο) → ο
Prim clsa : ι → ο
Prim clsh : ι → ο
Prim clcv : ι → ο
Prim clfn : ι → ο
Prim clk : ι → ο
Prim cld : ι → ο
Prim cops : ι → ο
Prim ccmtN : ι → ο
Prim col : ι → ο
Prim coml : ι → ο
Prim ccvr : ι → ο
Prim catm : ι → ο
Prim cal : ι → ο
Prim clc : ι → ο
Prim chlt : ι → ο
Prim clln : ι → ο
Prim clpl : ι → ο
Prim clvol : ι → ο
Prim clines : ι → ο
Prim cpointsN : ι → ο
Prim cpsubsp : ι → ο
Prim cpmap : ι → ο
Prim cpadd : ι → ο
Prim cpclN : ι → ο
Prim cpolN : ι → ο
Prim cpscN : ι → ο
Prim clh : ι → ο
Prim claut : ι → ο
Prim cwpointsN : ι → ο
Prim cpautN : ι → ο
Prim cldil : ι → ο
Prim cltrn : ι → ο
Prim cdilN : ι → ο
Prim ctrnN : ι → ο
Prim ctrl : ι → ο
Prim ctgrp : ι → ο
Prim ctendo : ι → ο
Prim cedring : ι → ο
Prim cedring_rN : ι → ο
Prim cdveca : ι → ο
Prim cdia : ι → ο
Prim cdvh : ι → ο
Prim cocaN : ι → ο
Prim cdjaN : ι → ο
Prim cdib : ι → ο
Prim cdic : ι → ο
Prim cdih : ι → ο
Prim coch : ι → ο
Prim cdjh : ι → ο
Prim clpoN : ι → ο
Prim clcd : ι → ο
Prim cmpd : ι → ο
Prim chvm : ι → ο
Prim chdma1 : ι → ο
Prim chdma : ι → ο
Prim chg : ι → ο
Prim chlh : ι → ο
Prim cnacs : ι → ο
Prim cmzpcl : ι → ο
Prim cmzp : ι → ο
Prim cdioph : ι → ο
Prim csquarenn : ι → ο
Prim cpell1qr : ι → ο
Prim cpell1234qr : ι → ο
Prim cpell14qr : ι → ο
Prim cpellfund : ι → ο
Prim crmx : ι → ο
Prim crmy : ι → ο
Prim clfig : ι → ο
Prim clnm : ι → ο
Prim clnr : ι → ο
Prim cldgis : ι → ο
Prim cmnc : ι → ο
Prim cplylt : ι → ο
Prim cdgraa : ι → ο
Prim cmpaa : ι → ο
Prim citgo : ι → ο
Prim cza : ι → ο
Prim cmend : ι → ο
Prim csdrg : ι → ο
Prim ccytp : ι → ο
Prim ctopsep : ι → ο
Prim ctoplnd : ι → ο
Prim crcl : ι → ο
Prim whe : (ι → ο) → (ι → ο) → ο
Prim cbcc : ι → ο
Prim cplusr : ι → ο
Prim cminusr : ι → ο
Prim ctimesr : ι → ο
Prim cptdfc : (ι → ο) → (ι → ο) → ι → ο
Prim crr3c : ι → ο
Prim cline3 : ι → ο
Prim wvd1 : ο → ο → ο
Prim wvd2 : ο → ο → ο → ο
Prim wvhc2 : ο → ο → ο
Prim wvd3 : ο → ο → ο → ο → ο
Prim wvhc3 : ο → ο → ο → ο
Prim wvhc4 : ο → ο → ο → ο → ο
Prim wvhc5 : ο → ο → ο → ο → ο → ο
Prim wvhc6 : ο → ο → ο → ο → ο → ο → ο
Prim wvhc7 : ο → ο → ο → ο → ο → ο → ο → ο
Prim wvhc8 : ο → ο → ο → ο → ο → ο → ο → ο → ο
Prim wvhc9 : ο → ο → ο → ο → ο → ο → ο → ο → ο → ο
Prim wvhc10 : ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο
Prim wvhc11 : ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο
Prim wvhc12 : ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο → ο
Prim clsi : ι → ο
Prim clsxlim : ι → ο
Prim csalg : ι → ο
Prim csalon : ι → ο
Prim csalgen : ι → ο
Prim csumge0 : ι → ο
Prim cmea : ι → ο
Prim come : ι → ο
Prim ccaragen : ι → ο
Prim covoln : ι → ο
Prim cvoln : ι → ο
Prim csmblfn : ι → ο
Prim wdfat : (ι → ο) → (ι → ο) → ο
Prim cafv : (ι → ο) → (ι → ο) → ι → ο
Prim caov : (ι → ο) → (ι → ο) → (ι → ο) → ι → ο
Prim cnelbr : ι → ο
Prim ciccp : ι → ο
Prim cpfx : ι → ο
Prim cfmtno : ι → ο
Prim ceven : ι → ο
Prim codd : ι → ο
Prim cgbe : ι → ο
Prim cgbow : ι → ο
Prim cgbo : ι → ο
Prim cupwlks : ι → ο
Prim cspr : ι → ο
Prim cmgmhm : ι → ο
Prim csubmgm : ι → ο
Prim ccllaw : ι → ο
Prim casslaw : ι → ο
Prim ccomlaw : ι → ο
Prim cintop : ι → ο
Prim cclintop : ι → ο
Prim cassintop : ι → ο
Prim cmgm2 : ι → ο
Prim ccmgm2 : ι → ο
Prim csgrp2 : ι → ο
Prim ccsgrp2 : ι → ο
Prim crng : ι → ο
Prim crngh : ι → ο
Prim crngs : ι → ο
Prim crngc : ι → ο
Prim crngcALTV : ι → ο
Prim cringc : ι → ο
Prim cringcALTV : ι → ο
Prim cdmatalt : ι → ο
Prim cscmatalt : ι → ο
Prim clinc : ι → ο
Prim clinco : ι → ο
Prim clininds : ι → ο
Prim clindeps : ι → ο
Prim cfdiv : ι → ο
Prim cbigo : ι → ο
Prim cblen : ι → ο
Prim cdig : ι → ο
Prim csetrecs : (ι → ο) → ι → ο
Prim cpg : ι → ο
Prim cge_real : ι → ο
Prim cgt : ι → ο
Prim csinh : ι → ο
Prim ccosh : ι → ο
Prim ctanh : ι → ο
Prim csec : ι → ο
Prim ccsc : ι → ο
Prim ccot : ι → ο
Prim clog_ : ι → ο
Prim wreflexive : (ι → ο) → (ι → ο) → ο
Prim wirreflexive : (ι → ο) → (ι → ο) → ο
Prim walsi : (ι → ο) → (ι → ο) → ο
Prim walsc : (ι → ο) → (ι → ι → ο) → ο
Axiom ax_mp__ax_1__ax_2__ax_3__df_bi__df_or__df_an__df_ifp__df_3or__df_3an__df_nan__df_xor__df_tru__df_fal__df_had__df_cad__df_ex__df_nf : ∀ x0 : ο . ((∀ x1 x2 : ο . x1 ⟶ (x1 ⟶ x2) ⟶ x2) ⟶ (∀ x1 x2 : ο . x1 ⟶ x2 ⟶ x1) ⟶ (∀ x1 x2 x3 : ο . (x1 ⟶ x2 ⟶ x3) ⟶ (x1 ⟶ x2) ⟶ x1 ⟶ x3) ⟶ (∀ x1 x2 : ο . (wn x1 ⟶ wn x2) ⟶ x2 ⟶ x1) ⟶ (∀ x1 x2 : ο . wn ((wb x1 x2 ⟶ wn ((x1 ⟶ x2) ⟶ wn (x2 ⟶ x1))) ⟶ wn (wn ((x1 ⟶ x2) ⟶ wn (x2 ⟶ x1)) ⟶ wb x1 x2))) ⟶ (∀ x1 x2 : ο . wb (wo x1 x2) (wn x1 ⟶ x2)) ⟶ (∀ x1 x2 : ο . wb (wa x1 x2) (wn (x1 ⟶ wn x2))) ⟶ (∀ x1 x2 x3 : ο . wb (wif x1 x2 x3) (wo (wa x1 x2) (wa (wn x1) x3))) ⟶ (∀ x1 x2 x3 : ο . wb (w3o x1 x2 x3) (wo (wo x1 x2) x3)) ⟶ (∀ x1 x2 x3 : ο . wb (w3a x1 x2 x3) (wa (wa x1 x2) x3)) ⟶ (∀ x1 x2 : ο . wb (wnan x1 x2) (wn (wa x1 x2))) ⟶ (∀ x1 x2 : ο . wb (wxo x1 x2) (wn (wb x1 x2))) ⟶ wb wtru ((∀ x1 . wceq (cv x1) (cv x1)) ⟶ ∀ x1 . wceq (cv x1) (cv x1)) ⟶ wb wfal (wn wtru) ⟶ (∀ x1 x2 x3 : ο . wb (whad x1 x2 x3) (wxo (wxo x1 x2) x3)) ⟶ (∀ x1 x2 x3 : ο . wb (wcad x1 x2 x3) (wo (wa x1 x2) (wa x3 (wxo x1 x2)))) ⟶ (∀ x1 : ι → ο . wb (wex x1) (wn (∀ x2 . wn (x1 x2)))) ⟶ (∀ x1 : ι → ο . wb (wnf x1) (wex x1 ⟶ ∀ x2 . x1 x2)) ⟶ x0) ⟶ x0
Axiom df_nfOLD__ax_gen__ax_4__ax_5__df_sb__df_sb_b__ax_6__ax_7__ax_7_b__ax_7_b1__ax_8__ax_8_b__ax_8_b1__ax_9__ax_9_b__ax_9_b1__ax_10__ax_11 : ∀ x0 : ο . ((∀ x1 : ι → ο . wb (wnfOLD x1) (∀ x2 . x1 x2 ⟶ ∀ x3 . x1 x3)) ⟶ (∀ x1 : ι → ο . (∀ x2 . x1 x2) ⟶ ∀ x2 . x1 x2) ⟶ (∀ x1 x2 : ι → ο . (∀ x3 . x1 x3 ⟶ x2 x3) ⟶ (∀ x3 . x1 x3) ⟶ ∀ x3 . x2 x3) ⟶ (∀ x1 : ο . x1 ⟶ ∀ x2 . x1) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 . wb (wsb x1 x2) (wa (wceq (cv x3) (cv x2) ⟶ x1 x3) (wex (λ x4 . wa (wceq (cv x4) (cv x2)) (x1 x4))))) ⟶ (∀ x1 : ι → ο . ∀ x2 . wb (wsb x1 x2) (wa (wceq (cv x2) (cv x2) ⟶ x1 x2) (wex (λ x3 . wa (wceq (cv x3) (cv x3)) (x1 x3))))) ⟶ (∀ x1 . wn (∀ x2 . wn (wceq (cv x2) (cv x1)))) ⟶ (∀ x1 x2 x3 . wceq (cv x1) (cv x2) ⟶ wceq (cv x1) (cv x3) ⟶ wceq (cv x2) (cv x3)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wceq (cv x1) (cv x1) ⟶ wceq (cv x2) (cv x1)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wceq (cv x1) (cv x2) ⟶ wceq (cv x2) (cv x2)) ⟶ (∀ x1 x2 x3 . wceq (cv x1) (cv x2) ⟶ wcel (cv x1) (cv x3) ⟶ wcel (cv x2) (cv x3)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wcel (cv x1) (cv x1) ⟶ wcel (cv x2) (cv x1)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wcel (cv x1) (cv x2) ⟶ wcel (cv x2) (cv x2)) ⟶ (∀ x1 x2 x3 . wceq (cv x1) (cv x2) ⟶ wcel (cv x3) (cv x1) ⟶ wcel (cv x3) (cv x2)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wcel (cv x1) (cv x1) ⟶ wcel (cv x1) (cv x2)) ⟶ (∀ x1 x2 . wceq (cv x1) (cv x2) ⟶ wcel (cv x2) (cv x1) ⟶ wcel (cv x2) (cv x2)) ⟶ (∀ x1 : ι → ο . wn (∀ x2 . x1 x2) ⟶ ∀ x2 . wn (∀ x3 . x1 x3)) ⟶ (∀ x1 : ι → ι → ο . (∀ x2 x3 . x1 x2 x3) ⟶ ∀ x2 x3 . x1 x3 x2) ⟶ x0) ⟶ x0
Axiom ax_11_b__ax_12__ax_12_b__ax_13__ax_13_b__df_eu__df_mo__ax_ext__df_clab__df_clab_b__df_cleq__df_clel__df_nfc__df_ne__df_nel__df_ral__df_rex__df_reu : ∀ x0 : ο . ((∀ x1 : ι → ο . (∀ x2 x3 . x1 x3) ⟶ ∀ x2 x3 . x1 x3) ⟶ (∀ x1 : ι → ι → ο . ∀ x2 x3 . wceq (cv x2) (cv x3) ⟶ (∀ x4 . x1 x2 x4) ⟶ ∀ x4 . wceq (cv x4) (cv x3) ⟶ x1 x4 x3) ⟶ (∀ x1 : ι → ο . ∀ x2 . wceq (cv x2) (cv x2) ⟶ (∀ x3 . x1 x3) ⟶ ∀ x3 . wceq (cv x3) (cv x3) ⟶ x1 x3) ⟶ (∀ x1 x2 x3 . wn (wceq (cv x3) (cv x1)) ⟶ wceq (cv x1) (cv x2) ⟶ ∀ x4 . wceq (cv x1) (cv x2)) ⟶ (∀ x1 x2 . wn (wceq (cv x2) (cv x2)) ⟶ wceq (cv x2) (cv x1) ⟶ ∀ x3 . wceq (cv x3) (cv x1)) ⟶ (∀ x1 : ι → ο . wb (weu x1) (wex (λ x2 . ∀ x3 . wb (x1 x3) (wceq (cv x3) (cv x2))))) ⟶ (∀ x1 : ι → ο . wb (wmo x1) (wex x1 ⟶ weu x1)) ⟶ (∀ x1 x2 . (∀ x3 . wb (wcel (cv x3) (cv x1)) (wcel (cv x3) (cv x2))) ⟶ wceq (cv x1) (cv x2)) ⟶ (∀ x1 : ι → ο . ∀ x2 . wb (wcel (cv x2) (cab x1)) (wsb x1 x2)) ⟶ (∀ x1 : ι → ο . ∀ x2 . wb (wcel (cv x2) (cab x1)) (wsb x1 x2)) ⟶ (∀ x1 x2 : ι → ι → ι → ο . (∀ x3 x4 . (∀ x5 . wb (wcel (cv x5) (cv x3)) (wcel (cv x5) (cv x4))) ⟶ wceq (cv x3) (cv x4)) ⟶ ∀ x3 x4 . wb (wceq (x1 x3 x4) (x2 x3 x4)) (∀ x5 . wb (wcel (cv x5) (x1 x3 x4)) (wcel (cv x5) (x2 x3 x4)))) ⟶ (∀ x1 x2 : ι → ο . wb (wcel x1 x2) (wex (λ x3 . wa (wceq (cv x3) x1) (wcel (cv x3) x2)))) ⟶ (∀ x1 : ι → ι → ο . wb (wnfc x1) (∀ x2 . wnf (λ x3 . wcel (cv x2) (x1 x3)))) ⟶ (∀ x1 x2 : ι → ο . wb (wne x1 x2) (wn (wceq x1 x2))) ⟶ (∀ x1 x2 : ι → ο . wb (wnel x1 x2) (wn (wcel x1 x2))) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (wral x1 x2) (∀ x3 . wcel (cv x3) (x2 x3) ⟶ x1 x3)) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (wrex x1 x2) (wex (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3)))) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (wreu x1 x2) (weu (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3)))) ⟶ x0) ⟶ x0
Axiom df_rmo__df_rab__df_v__df_cdeq__df_sbc__df_csb__df_dif__df_un__df_in__df_ss__df_pss__df_symdif__df_nul__df_if__df_pw__df_sn__df_pr__df_tp : ∀ x0 : ο . ((∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (wrmo x1 x2) (wmo (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3)))) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wceq (crab x1 x2) (cab (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3)))) ⟶ wceq cvv (cab (λ x1 . wceq (cv x1) (cv x1))) ⟶ (∀ x1 : ο . ∀ x2 x3 . wb (wcdeq x1 x2 x3) (wceq (cv x2) (cv x3) ⟶ x1)) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . ∀ x3 . wb (wsbc x1 (x2 x3)) (wcel (x2 x3) (cab x1))) ⟶ (∀ x1 x2 : ι → ι → ο . ∀ x3 . wceq (csb (x1 x3) x2) (cab (λ x4 . wsbc (λ x5 . wcel (cv x4) (x2 x5)) (x1 x3)))) ⟶ (∀ x1 x2 : ι → ο . wceq (cdif x1 x2) (cab (λ x3 . wa (wcel (cv x3) x1) (wn (wcel (cv x3) x2))))) ⟶ (∀ x1 x2 : ι → ο . wceq (cun x1 x2) (cab (λ x3 . wo (wcel (cv x3) x1) (wcel (cv x3) x2)))) ⟶ (∀ x1 x2 : ι → ο . wceq (cin x1 x2) (cab (λ x3 . wa (wcel (cv x3) x1) (wcel (cv x3) x2)))) ⟶ (∀ x1 x2 : ι → ο . wb (wss x1 x2) (wceq (cin x1 x2) x1)) ⟶ (∀ x1 x2 : ι → ο . wb (wpss x1 x2) (wa (wss x1 x2) (wne x1 x2))) ⟶ (∀ x1 x2 : ι → ο . wceq (csymdif x1 x2) (cun (cdif x1 x2) (cdif x2 x1))) ⟶ wceq c0 (cdif cvv cvv) ⟶ (∀ x1 : ο . ∀ x2 x3 : ι → ο . wceq (cif x1 x2 x3) (cab (λ x4 . wo (wa (wcel (cv x4) x2) x1) (wa (wcel (cv x4) x3) (wn x1))))) ⟶ (∀ x1 : ι → ο . wceq (cpw x1) (cab (λ x2 . wss (cv x2) x1))) ⟶ (∀ x1 : ι → ο . wceq (csn x1) (cab (λ x2 . wceq (cv x2) x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (cpr x1 x2) (cun (csn x1) (csn x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (ctp x1 x2 x3) (cun (cpr x1 x2) (csn x3))) ⟶ x0) ⟶ x0
Axiom df_op__df_ot__df_uni__df_int__df_iun__df_iin__df_disj__df_br__df_opab__df_opab_b__df_mpt__df_tr__ax_rep__ax_pow__df_id__df_eprel__df_po__df_so : ∀ x0 : ο . ((∀ x1 x2 : ι → ο . wceq (cop x1 x2) (cab (λ x3 . w3a (wcel x1 cvv) (wcel x2 cvv) (wcel (cv x3) (cpr (csn x1) (cpr x1 x2)))))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cotp x1 x2 x3) (cop (cop x1 x2) x3)) ⟶ (∀ x1 : ι → ο . wceq (cuni x1) (cab (λ x2 . wex (λ x3 . wa (wcel (cv x2) (cv x3)) (wcel (cv x3) x1))))) ⟶ (∀ x1 : ι → ο . wceq (cint x1) (cab (λ x2 . ∀ x3 . wcel (cv x3) x1 ⟶ wcel (cv x2) (cv x3)))) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (ciun x1 x2) (cab (λ x3 . wrex (λ x4 . wcel (cv x3) (x2 x4)) x1))) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (ciin x1 x2) (cab (λ x3 . wral (λ x4 . wcel (cv x3) (x2 x4)) x1))) ⟶ (∀ x1 x2 : ι → ι → ο . wb (wdisj x1 x2) (∀ x3 . wrmo (λ x4 . wcel (cv x3) (x2 x4)) x1)) ⟶ (∀ x1 x2 x3 : ι → ο . wb (wbr x1 x2 x3) (wcel (cop x1 x2) x3)) ⟶ (∀ x1 : ι → ι → ο . wceq (copab x1) (cab (λ x2 . wex (λ x3 . wex (λ x4 . wa (wceq (cv x2) (cop (cv x3) (cv x4))) (x1 x3 x4)))))) ⟶ (∀ x1 : ι → ο . wceq (copab_b x1) (cab (λ x2 . wex (λ x3 . wex (λ x4 . wa (wceq (cv x2) (cop (cv x4) (cv x4))) (x1 x4)))))) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (cmpt x1 x2) (copab (λ x3 x4 . wa (wcel (cv x3) (x1 x3)) (wceq (cv x4) (x2 x3))))) ⟶ (∀ x1 : ι → ο . wb (wtr x1) (wss (cuni x1) x1)) ⟶ (∀ x1 : ι → ι → ι → ο . ∀ x2 . (∀ x3 . wex (λ x4 . ∀ x5 . (∀ x6 . x1 x6 x5 x3) ⟶ wceq (cv x5) (cv x4))) ⟶ wex (λ x3 . ∀ x4 . wb (wcel (cv x4) (cv x3)) (wex (λ x5 . wa (wcel (cv x5) (cv x2)) (∀ x6 . x1 x6 x4 x5))))) ⟶ (∀ x1 . wex (λ x2 . ∀ x3 . (∀ x4 . wcel (cv x4) (cv x3) ⟶ wcel (cv x4) (cv x1)) ⟶ wcel (cv x3) (cv x2))) ⟶ wceq cid (copab (λ x1 x2 . wceq (cv x1) (cv x2))) ⟶ wceq cep (copab (λ x1 x2 . wcel (cv x1) (cv x2))) ⟶ (∀ x1 x2 : ι → ο . wb (wpo x1 x2) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wa (wn (wbr (cv x3) (cv x3) x2)) (wa (wbr (cv x3) (cv x4) x2) (wbr (cv x4) (cv x5) x2) ⟶ wbr (cv x3) (cv x5) x2)) (λ x5 . x1)) (λ x4 . x1)) (λ x3 . x1))) ⟶ (∀ x1 x2 : ι → ο . wb (wor x1 x2) (wa (wpo x1 x2) (wral (λ x3 . wral (λ x4 . w3o (wbr (cv x3) (cv x4) x2) (wceq (cv x3) (cv x4)) (wbr (cv x4) (cv x3) x2)) (λ x4 . x1)) (λ x3 . x1)))) ⟶ x0) ⟶ x0
Axiom df_fr__df_se__df_we__df_xp__df_rel__df_cnv__df_co__df_dm__df_rn__df_res__df_ima__df_pred__df_ord__df_on__df_lim__df_suc__df_iota__df_fun : ∀ x0 : ο . ((∀ x1 x2 : ι → ο . wb (wfr x1 x2) (∀ x3 . wa (wss (cv x3) x1) (wne (cv x3) c0) ⟶ wrex (λ x4 . wral (λ x5 . wn (wbr (cv x5) (cv x4) x2)) (λ x5 . cv x3)) (λ x4 . cv x3))) ⟶ (∀ x1 x2 : ι → ο . wb (wse x1 x2) (wral (λ x3 . wcel (crab (λ x4 . wbr (cv x4) (cv x3) x2) (λ x4 . x1)) cvv) (λ x3 . x1))) ⟶ (∀ x1 x2 : ι → ο . wb (wwe x1 x2) (wa (wfr x1 x2) (wor x1 x2))) ⟶ (∀ x1 x2 : ι → ο . wceq (cxp x1 x2) (copab (λ x3 x4 . wa (wcel (cv x3) x1) (wcel (cv x4) x2)))) ⟶ (∀ x1 : ι → ο . wb (wrel x1) (wss x1 (cxp cvv cvv))) ⟶ (∀ x1 : ι → ο . wceq (ccnv x1) (copab (λ x2 x3 . wbr (cv x3) (cv x2) x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (ccom x1 x2) (copab (λ x3 x4 . wex (λ x5 . wa (wbr (cv x3) (cv x5) x2) (wbr (cv x5) (cv x4) x1))))) ⟶ (∀ x1 : ι → ο . wceq (cdm x1) (cab (λ x2 . wex (λ x3 . wbr (cv x2) (cv x3) x1)))) ⟶ (∀ x1 : ι → ο . wceq (crn x1) (cdm (ccnv x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (cres x1 x2) (cin x1 (cxp x2 cvv))) ⟶ (∀ x1 x2 : ι → ο . wceq (cima x1 x2) (crn (cres x1 x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cpred x1 x2 x3) (cin x1 (cima (ccnv x2) (csn x3)))) ⟶ (∀ x1 : ι → ο . wb (word x1) (wa (wtr x1) (wwe x1 cep))) ⟶ wceq con0 (cab (λ x1 . word (cv x1))) ⟶ (∀ x1 : ι → ο . wb (wlim x1) (w3a (word x1) (wne x1 c0) (wceq x1 (cuni x1)))) ⟶ (∀ x1 : ι → ο . wceq (csuc x1) (cun x1 (csn x1))) ⟶ (∀ x1 : ι → ο . wceq (cio x1) (cuni (cab (λ x2 . wceq (cab x1) (csn (cv x2)))))) ⟶ (∀ x1 : ι → ο . wb (wfun x1) (wa (wrel x1) (wss (ccom x1 (ccnv x1)) cid))) ⟶ x0) ⟶ x0
Axiom df_fn__df_f__df_f1__df_fo__df_f1o__df_fv__df_isom__df_riota__df_ov__df_oprab__df_mpt2__df_of__df_ofr__df_rpss__ax_un__df_om__df_1st__df_2nd : ∀ x0 : ο . ((∀ x1 x2 : ι → ο . wb (wfn x1 x2) (wa (wfun x1) (wceq (cdm x1) x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wb (wf x1 x2 x3) (wa (wfn x3 x1) (wss (crn x3) x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wb (wf1 x1 x2 x3) (wa (wf x1 x2 x3) (wfun (ccnv x3)))) ⟶ (∀ x1 x2 x3 : ι → ο . wb (wfo x1 x2 x3) (wa (wfn x3 x1) (wceq (crn x3) x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wb (wf1o x1 x2 x3) (wa (wf1 x1 x2 x3) (wfo x1 x2 x3))) ⟶ (∀ x1 x2 : ι → ο . wceq (cfv x1 x2) (cio (λ x3 . wbr x1 (cv x3) x2))) ⟶ (∀ x1 x2 x3 x4 x5 : ι → ο . wb (wiso x1 x2 x3 x4 x5) (wa (wf1o x1 x2 x5) (wral (λ x6 . wral (λ x7 . wb (wbr (cv x6) (cv x7) x3) (wbr (cfv (cv x6) x5) (cfv (cv x7) x5) x4)) (λ x7 . x1)) (λ x6 . x1)))) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wceq (crio x1 x2) (cio (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3)))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (co x1 x2 x3) (cfv (cop x1 x2) x3)) ⟶ (∀ x1 : ι → ι → ι → ο . wceq (coprab x1) (cab (λ x2 . wex (λ x3 . wex (λ x4 . wex (λ x5 . wa (wceq (cv x2) (cop (cop (cv x3) (cv x4)) (cv x5))) (x1 x3 x4 x5))))))) ⟶ (∀ x1 x2 x3 : ι → ι → ι → ο . wceq (cmpt2 x1 x2 x3) (coprab (λ x4 x5 x6 . wa (wa (wcel (cv x4) (x1 x4 x5)) (wcel (cv x5) (x2 x4 x5))) (wceq (cv x6) (x3 x4 x5))))) ⟶ (∀ x1 : ι → ο . wceq (cof x1) (cmpt2 (λ x2 x3 . cvv) (λ x2 x3 . cvv) (λ x2 x3 . cmpt (λ x4 . cin (cdm (cv x2)) (cdm (cv x3))) (λ x4 . co (cfv (cv x4) (cv x2)) (cfv (cv x4) (cv x3)) x1)))) ⟶ (∀ x1 : ι → ο . wceq (cofr x1) (copab (λ x2 x3 . wral (λ x4 . wbr (cfv (cv x4) (cv x2)) (cfv (cv x4) (cv x3)) x1) (λ x4 . cin (cdm (cv x2)) (cdm (cv x3)))))) ⟶ wceq crpss (copab (λ x1 x2 . wpss (cv x1) (cv x2))) ⟶ (∀ x1 . wex (λ x2 . ∀ x3 . wex (λ x4 . wa (wcel (cv x3) (cv x4)) (wcel (cv x4) (cv x1))) ⟶ wcel (cv x3) (cv x2))) ⟶ wceq com (crab (λ x1 . ∀ x2 . wlim (cv x2) ⟶ wcel (cv x1) (cv x2)) (λ x1 . con0)) ⟶ wceq c1st (cmpt (λ x1 . cvv) (λ x1 . cuni (cdm (csn (cv x1))))) ⟶ wceq c2nd (cmpt (λ x1 . cvv) (λ x1 . cuni (crn (csn (cv x1))))) ⟶ x0) ⟶ x0
Axiom df_supp__df_tpos__df_cur__df_unc__df_undef__df_wrecs__df_smo__df_recs__df_rdg__df_seqom__df_1o__df_2o__df_3o__df_4o__df_oadd__df_omul__df_oexp__df_er : ∀ x0 : ο . (wceq csupp (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wne (cima (cv x1) (csn (cv x3))) (csn (cv x2))) (λ x3 . cdm (cv x1)))) ⟶ (∀ x1 : ι → ο . wceq (ctpos x1) (ccom x1 (cmpt (λ x2 . cun (ccnv (cdm x1)) (csn c0)) (λ x2 . cuni (ccnv (csn (cv x2))))))) ⟶ (∀ x1 : ι → ο . wceq (ccur x1) (cmpt (λ x2 . cdm (cdm x1)) (λ x2 . copab (λ x3 x4 . wbr (cop (cv x2) (cv x3)) (cv x4) x1)))) ⟶ (∀ x1 : ι → ο . wceq (cunc x1) (coprab (λ x2 x3 x4 . wbr (cv x3) (cv x4) (cfv (cv x2) x1)))) ⟶ wceq cund (cmpt (λ x1 . cvv) (λ x1 . cpw (cuni (cv x1)))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cwrecs x1 x2 x3) (cuni (cab (λ x4 . wex (λ x5 . w3a (wfn (cv x4) (cv x5)) (wa (wss (cv x5) x1) (wral (λ x6 . wss (cpred x1 x2 (cv x6)) (cv x5)) (λ x6 . cv x5))) (wral (λ x6 . wceq (cfv (cv x6) (cv x4)) (cfv (cres (cv x4) (cpred x1 x2 (cv x6))) x3)) (λ x6 . cv x5))))))) ⟶ (∀ x1 : ι → ο . wb (wsmo x1) (w3a (wf (cdm x1) con0 x1) (word (cdm x1)) (wral (λ x2 . wral (λ x3 . wcel (cv x2) (cv x3) ⟶ wcel (cfv (cv x2) x1) (cfv (cv x3) x1)) (λ x3 . cdm x1)) (λ x2 . cdm x1)))) ⟶ (∀ x1 : ι → ο . wceq (crecs x1) (cwrecs con0 cep x1)) ⟶ (∀ x1 x2 : ι → ο . wceq (crdg x1 x2) (crecs (cmpt (λ x3 . cvv) (λ x3 . cif (wceq (cv x3) c0) x2 (cif (wlim (cdm (cv x3))) (cuni (crn (cv x3))) (cfv (cfv (cuni (cdm (cv x3))) (cv x3)) x1)))))) ⟶ (∀ x1 x2 : ι → ο . wceq (cseqom x1 x2) (cima (crdg (cmpt2 (λ x3 x4 . com) (λ x3 x4 . cvv) (λ x3 x4 . cop (csuc (cv x3)) (co (cv x3) (cv x4) x1))) (cop c0 (cfv x2 cid))) com)) ⟶ wceq c1o (csuc c0) ⟶ wceq c2o (csuc c1o) ⟶ wceq c3o (csuc c2o) ⟶ wceq c4o (csuc c3o) ⟶ wceq coa (cmpt2 (λ x1 x2 . con0) (λ x1 x2 . con0) (λ x1 x2 . cfv (cv x2) (crdg (cmpt (λ x3 . cvv) (λ x3 . csuc (cv x3))) (cv x1)))) ⟶ wceq comu (cmpt2 (λ x1 x2 . con0) (λ x1 x2 . con0) (λ x1 x2 . cfv (cv x2) (crdg (cmpt (λ x3 . cvv) (λ x3 . co (cv x3) (cv x1) coa)) c0))) ⟶ wceq coe (cmpt2 (λ x1 x2 . con0) (λ x1 x2 . con0) (λ x1 x2 . cif (wceq (cv x1) c0) (cdif c1o (cv x2)) (cfv (cv x2) (crdg (cmpt (λ x3 . cvv) (λ x3 . co (cv x3) (cv x1) comu)) c1o)))) ⟶ (∀ x1 x2 : ι → ο . wb (wer x1 x2) (w3a (wrel x2) (wceq (cdm x2) x1) (wss (cun (ccnv x2) (ccom x2 x2)) x2))) ⟶ x0) ⟶ x0
Axiom df_ec__df_qs__df_map__df_pm__df_ixp__df_en__df_dom__df_sdom__df_fin__df_fsupp__df_fi__df_sup__df_inf__df_oi__df_har__df_wdom__ax_reg__ax_inf : ∀ x0 : ο . ((∀ x1 x2 : ι → ο . wceq (cec x1 x2) (cima x2 (csn x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (cqs x1 x2) (cab (λ x3 . wrex (λ x4 . wceq (cv x3) (cec (cv x4) x2)) (λ x4 . x1)))) ⟶ wceq cmap (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cab (λ x3 . wf (cv x2) (cv x1) (cv x3)))) ⟶ wceq cpm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wfun (cv x3)) (λ x3 . cpw (cxp (cv x2) (cv x1))))) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (cixp x1 x2) (cab (λ x3 . wa (wfn (cv x3) (cab (λ x4 . wcel (cv x4) (x1 x4)))) (wral (λ x4 . wcel (cfv (cv x4) (cv x3)) (x2 x4)) x1)))) ⟶ wceq cen (copab (λ x1 x2 . wex (λ x3 . wf1o (cv x1) (cv x2) (cv x3)))) ⟶ wceq cdom (copab (λ x1 x2 . wex (λ x3 . wf1 (cv x1) (cv x2) (cv x3)))) ⟶ wceq csdm (cdif cdom cen) ⟶ wceq cfn (cab (λ x1 . wrex (λ x2 . wbr (cv x1) (cv x2) cen) (λ x2 . com))) ⟶ wceq cfsupp (copab (λ x1 x2 . wa (wfun (cv x1)) (wcel (co (cv x1) (cv x2) csupp) cfn))) ⟶ wceq cfi (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wrex (λ x3 . wceq (cv x2) (cint (cv x3))) (λ x3 . cin (cpw (cv x1)) cfn)))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (csup x1 x2 x3) (cuni (crab (λ x4 . wa (wral (λ x5 . wn (wbr (cv x4) (cv x5) x3)) (λ x5 . x1)) (wral (λ x5 . wbr (cv x5) (cv x4) x3 ⟶ wrex (λ x6 . wbr (cv x5) (cv x6) x3) (λ x6 . x1)) (λ x5 . x2))) (λ x4 . x2)))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cinf x1 x2 x3) (csup x1 x2 (ccnv x3))) ⟶ (∀ x1 x2 : ι → ο . wceq (coi x1 x2) (cif (wa (wwe x1 x2) (wse x1 x2)) (cres (crecs (cmpt (λ x3 . cvv) (λ x3 . crio (λ x4 . wral (λ x5 . wn (wbr (cv x5) (cv x4) x2)) (λ x5 . crab (λ x6 . wral (λ x7 . wbr (cv x7) (cv x6) x2) (λ x7 . crn (cv x3))) (λ x6 . x1))) (λ x4 . crab (λ x5 . wral (λ x6 . wbr (cv x6) (cv x5) x2) (λ x6 . crn (cv x3))) (λ x5 . x1))))) (crab (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cv x5) (cv x4) x2) (λ x5 . cima (crecs (cmpt (λ x6 . cvv) (λ x6 . crio (λ x7 . wral (λ x8 . wn (wbr (cv x8) (cv x7) x2)) (λ x8 . crab (λ x9 . wral (λ x10 . wbr (cv x10) (cv x9) x2) (λ x10 . crn (cv x6))) (λ x9 . x1))) (λ x7 . crab (λ x8 . wral (λ x9 . wbr (cv x9) (cv x8) x2) (λ x9 . crn (cv x6))) (λ x8 . x1))))) (cv x3))) (λ x4 . x1)) (λ x3 . con0))) c0)) ⟶ wceq char (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cv x2) (cv x1) cdom) (λ x2 . con0))) ⟶ wceq cwdom (copab (λ x1 x2 . wo (wceq (cv x1) c0) (wex (λ x3 . wfo (cv x2) (cv x1) (cv x3))))) ⟶ (∀ x1 . wex (λ x2 . wcel (cv x2) (cv x1)) ⟶ wex (λ x2 . wa (wcel (cv x2) (cv x1)) (∀ x3 . wcel (cv x3) (cv x2) ⟶ wn (wcel (cv x3) (cv x1))))) ⟶ (∀ x1 . wex (λ x2 . wa (wcel (cv x1) (cv x2)) (∀ x3 . wcel (cv x3) (cv x2) ⟶ wex (λ x4 . wa (wcel (cv x3) (cv x4)) (wcel (cv x4) (cv x2)))))) ⟶ x0) ⟶ x0
Axiom ax_inf2__df_cnf__df_tc__df_r1__df_rank__df_card__df_aleph__df_cf__df_acn__df_ac__df_cda__df_fin1a__df_fin2__df_fin4__df_fin3__df_fin5__df_fin6__df_fin7 : ∀ x0 : ο . (wex (λ x1 . wa (wex (λ x2 . wa (wcel (cv x2) (cv x1)) (∀ x3 . wn (wcel (cv x3) (cv x2))))) (∀ x2 . wcel (cv x2) (cv x1) ⟶ wex (λ x3 . wa (wcel (cv x3) (cv x1)) (∀ x4 . wb (wcel (cv x4) (cv x3)) (wo (wcel (cv x4) (cv x2)) (wceq (cv x4) (cv x2))))))) ⟶ wceq ccnf (cmpt2 (λ x1 x2 . con0) (λ x1 x2 . con0) (λ x1 x2 . cmpt (λ x3 . crab (λ x4 . wbr (cv x4) c0 cfsupp) (λ x4 . co (cv x1) (cv x2) cmap)) (λ x3 . csb (coi (co (cv x3) c0 csupp) cep) (λ x4 . cfv (cdm (cv x4)) (cseqom (cmpt2 (λ x5 x6 . cvv) (λ x5 x6 . cvv) (λ x5 x6 . co (co (co (cv x1) (cfv (cv x5) (cv x4)) coe) (cfv (cfv (cv x5) (cv x4)) (cv x3)) comu) (cv x6) coa)) c0))))) ⟶ wceq ctc (cmpt (λ x1 . cvv) (λ x1 . cint (cab (λ x2 . wa (wss (cv x1) (cv x2)) (wtr (cv x2)))))) ⟶ wceq cr1 (crdg (cmpt (λ x1 . cvv) (λ x1 . cpw (cv x1))) c0) ⟶ wceq crnk (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wcel (cv x1) (cfv (csuc (cv x2)) cr1)) (λ x2 . con0)))) ⟶ wceq ccrd (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wbr (cv x2) (cv x1) cen) (λ x2 . con0)))) ⟶ wceq cale (crdg char com) ⟶ wceq ccf (cmpt (λ x1 . con0) (λ x1 . cint (cab (λ x2 . wex (λ x3 . wa (wceq (cv x2) (cfv (cv x3) ccrd)) (wa (wss (cv x3) (cv x1)) (wral (λ x4 . wrex (λ x5 . wss (cv x4) (cv x5)) (λ x5 . cv x3)) (λ x4 . cv x1)))))))) ⟶ (∀ x1 : ι → ο . wceq (wacn x1) (cab (λ x2 . wa (wcel x1 cvv) (wral (λ x3 . wex (λ x4 . wral (λ x5 . wcel (cfv (cv x5) (cv x4)) (cfv (cv x5) (cv x3))) (λ x5 . x1))) (λ x3 . co (cdif (cpw (cv x2)) (csn c0)) x1 cmap))))) ⟶ wb wac (∀ x1 . wex (λ x2 . wa (wss (cv x2) (cv x1)) (wfn (cv x2) (cdm (cv x1))))) ⟶ wceq ccda (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cun (cxp (cv x1) (csn c0)) (cxp (cv x2) (csn c1o)))) ⟶ wceq cfin1a (cab (λ x1 . wral (λ x2 . wo (wcel (cv x2) cfn) (wcel (cdif (cv x1) (cv x2)) cfn)) (λ x2 . cpw (cv x1)))) ⟶ wceq cfin2 (cab (λ x1 . wral (λ x2 . wa (wne (cv x2) c0) (wor (cv x2) crpss) ⟶ wcel (cuni (cv x2)) (cv x2)) (λ x2 . cpw (cpw (cv x1))))) ⟶ wceq cfin4 (cab (λ x1 . wn (wex (λ x2 . wa (wpss (cv x2) (cv x1)) (wbr (cv x2) (cv x1) cen))))) ⟶ wceq cfin3 (cab (λ x1 . wcel (cpw (cv x1)) cfin4)) ⟶ wceq cfin5 (cab (λ x1 . wo (wceq (cv x1) c0) (wbr (cv x1) (co (cv x1) (cv x1) ccda) csdm))) ⟶ wceq cfin6 (cab (λ x1 . wo (wbr (cv x1) c2o csdm) (wbr (cv x1) (cxp (cv x1) (cv x1)) csdm))) ⟶ wceq cfin7 (cab (λ x1 . wn (wrex (λ x2 . wbr (cv x1) (cv x2) cen) (λ x2 . cdif con0 com)))) ⟶ x0) ⟶ x0
Axiom ax_cc__ax_dc__ax_ac__ax_ac2__df_gch__df_wina__df_ina__df_wun__df_wunc__df_tsk__df_gru__ax_groth__df_tskm__df_ni__df_pli__df_mi__df_lti__df_plpq : ∀ x0 : ο . ((∀ x1 . wbr (cv x1) com cen ⟶ wex (λ x2 . wral (λ x3 . wne (cv x3) c0 ⟶ wcel (cfv (cv x3) (cv x2)) (cv x3)) (λ x3 . cv x1))) ⟶ (∀ x1 . wa (wex (λ x2 . wex (λ x3 . wbr (cv x2) (cv x3) (cv x1)))) (wss (crn (cv x1)) (cdm (cv x1))) ⟶ wex (λ x2 . wral (λ x3 . wbr (cfv (cv x3) (cv x2)) (cfv (csuc (cv x3)) (cv x2)) (cv x1)) (λ x3 . com))) ⟶ (∀ x1 . wex (λ x2 . ∀ x3 x4 . wa (wcel (cv x3) (cv x4)) (wcel (cv x4) (cv x1)) ⟶ wex (λ x5 . ∀ x6 . wb (wex (λ x7 . wa (wa (wcel (cv x6) (cv x4)) (wcel (cv x4) (cv x7))) (wa (wcel (cv x6) (cv x7)) (wcel (cv x7) (cv x2))))) (wceq (cv x6) (cv x5))))) ⟶ (∀ x1 . wex (λ x2 . ∀ x3 . wex (λ x4 . ∀ x5 . wo (wa (wcel (cv x2) (cv x1)) (wcel (cv x3) (cv x2) ⟶ wa (wa (wcel (cv x4) (cv x1)) (wn (wceq (cv x2) (cv x4)))) (wcel (cv x3) (cv x4)))) (wa (wn (wcel (cv x2) (cv x1))) (wcel (cv x3) (cv x1) ⟶ wa (wa (wcel (cv x4) (cv x3)) (wcel (cv x4) (cv x2))) (wa (wcel (cv x5) (cv x3)) (wcel (cv x5) (cv x2)) ⟶ wceq (cv x5) (cv x4))))))) ⟶ wceq cgch (cun cfn (cab (λ x1 . ∀ x2 . wn (wa (wbr (cv x1) (cv x2) csdm) (wbr (cv x2) (cpw (cv x1)) csdm))))) ⟶ wceq cwina (cab (λ x1 . w3a (wne (cv x1) c0) (wceq (cfv (cv x1) ccf) (cv x1)) (wral (λ x2 . wrex (λ x3 . wbr (cv x2) (cv x3) csdm) (λ x3 . cv x1)) (λ x2 . cv x1)))) ⟶ wceq cina (cab (λ x1 . w3a (wne (cv x1) c0) (wceq (cfv (cv x1) ccf) (cv x1)) (wral (λ x2 . wbr (cpw (cv x2)) (cv x1) csdm) (λ x2 . cv x1)))) ⟶ wceq cwun (cab (λ x1 . w3a (wtr (cv x1)) (wne (cv x1) c0) (wral (λ x2 . w3a (wcel (cuni (cv x2)) (cv x1)) (wcel (cpw (cv x2)) (cv x1)) (wral (λ x3 . wcel (cpr (cv x2) (cv x3)) (cv x1)) (λ x3 . cv x1))) (λ x2 . cv x1)))) ⟶ wceq cwunm (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wss (cv x1) (cv x2)) (λ x2 . cwun)))) ⟶ wceq ctsk (cab (λ x1 . wa (wral (λ x2 . wa (wss (cpw (cv x2)) (cv x1)) (wrex (λ x3 . wss (cpw (cv x2)) (cv x3)) (λ x3 . cv x1))) (λ x2 . cv x1)) (wral (λ x2 . wo (wbr (cv x2) (cv x1) cen) (wcel (cv x2) (cv x1))) (λ x2 . cpw (cv x1))))) ⟶ wceq cgru (cab (λ x1 . wa (wtr (cv x1)) (wral (λ x2 . w3a (wcel (cpw (cv x2)) (cv x1)) (wral (λ x3 . wcel (cpr (cv x2) (cv x3)) (cv x1)) (λ x3 . cv x1)) (wral (λ x3 . wcel (cuni (crn (cv x3))) (cv x1)) (λ x3 . co (cv x1) (cv x2) cmap))) (λ x2 . cv x1)))) ⟶ (∀ x1 . wex (λ x2 . w3a (wcel (cv x1) (cv x2)) (wral (λ x3 . wa (∀ x4 . wss (cv x4) (cv x3) ⟶ wcel (cv x4) (cv x2)) (wrex (λ x4 . ∀ x5 . wss (cv x5) (cv x3) ⟶ wcel (cv x5) (cv x4)) (λ x4 . cv x2))) (λ x3 . cv x2)) (∀ x3 . wss (cv x3) (cv x2) ⟶ wo (wbr (cv x3) (cv x2) cen) (wcel (cv x3) (cv x2))))) ⟶ wceq ctskm (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wcel (cv x1) (cv x2)) (λ x2 . ctsk)))) ⟶ wceq cnpi (cdif com (csn c0)) ⟶ wceq cpli (cres coa (cxp cnpi cnpi)) ⟶ wceq cmi (cres comu (cxp cnpi cnpi)) ⟶ wceq clti (cin cep (cxp cnpi cnpi)) ⟶ wceq cplpq (cmpt2 (λ x1 x2 . cxp cnpi cnpi) (λ x1 x2 . cxp cnpi cnpi) (λ x1 x2 . cop (co (co (cfv (cv x1) c1st) (cfv (cv x2) c2nd) cmi) (co (cfv (cv x2) c1st) (cfv (cv x1) c2nd) cmi) cpli) (co (cfv (cv x1) c2nd) (cfv (cv x2) c2nd) cmi))) ⟶ x0) ⟶ x0
Axiom df_mpq__df_ltpq__df_enq__df_nq__df_erq__df_plq__df_mq__df_1nq__df_rq__df_ltnq__df_np__df_1p__df_plp__df_mp__df_ltp__df_enr__df_nr__df_plr : ∀ x0 : ο . (wceq cmpq (cmpt2 (λ x1 x2 . cxp cnpi cnpi) (λ x1 x2 . cxp cnpi cnpi) (λ x1 x2 . cop (co (cfv (cv x1) c1st) (cfv (cv x2) c1st) cmi) (co (cfv (cv x1) c2nd) (cfv (cv x2) c2nd) cmi))) ⟶ wceq cltpq (copab (λ x1 x2 . wa (wa (wcel (cv x1) (cxp cnpi cnpi)) (wcel (cv x2) (cxp cnpi cnpi))) (wbr (co (cfv (cv x1) c1st) (cfv (cv x2) c2nd) cmi) (co (cfv (cv x2) c1st) (cfv (cv x1) c2nd) cmi) clti))) ⟶ wceq ceq (copab (λ x1 x2 . wa (wa (wcel (cv x1) (cxp cnpi cnpi)) (wcel (cv x2) (cxp cnpi cnpi))) (wex (λ x3 . wex (λ x4 . wex (λ x5 . wex (λ x6 . wa (wa (wceq (cv x1) (cop (cv x3) (cv x4))) (wceq (cv x2) (cop (cv x5) (cv x6)))) (wceq (co (cv x3) (cv x6) cmi) (co (cv x4) (cv x5) cmi))))))))) ⟶ wceq cnq (crab (λ x1 . wral (λ x2 . wbr (cv x1) (cv x2) ceq ⟶ wn (wbr (cfv (cv x2) c2nd) (cfv (cv x1) c2nd) clti)) (λ x2 . cxp cnpi cnpi)) (λ x1 . cxp cnpi cnpi)) ⟶ wceq cerq (cin ceq (cxp (cxp cnpi cnpi) cnq)) ⟶ wceq cplq (cres (ccom cerq cplpq) (cxp cnq cnq)) ⟶ wceq cmq (cres (ccom cerq cmpq) (cxp cnq cnq)) ⟶ wceq c1q (cop c1o c1o) ⟶ wceq crq (cima (ccnv cmq) (csn c1q)) ⟶ wceq cltq (cin cltpq (cxp cnq cnq)) ⟶ wceq cnp (cab (λ x1 . wa (wa (wpss c0 (cv x1)) (wpss (cv x1) cnq)) (wral (λ x2 . wa (∀ x3 . wbr (cv x3) (cv x2) cltq ⟶ wcel (cv x3) (cv x1)) (wrex (λ x3 . wbr (cv x2) (cv x3) cltq) (λ x3 . cv x1))) (λ x2 . cv x1)))) ⟶ wceq c1p (cab (λ x1 . wbr (cv x1) c1q cltq)) ⟶ wceq cpp (cmpt2 (λ x1 x2 . cnp) (λ x1 x2 . cnp) (λ x1 x2 . cab (λ x3 . wrex (λ x4 . wrex (λ x5 . wceq (cv x3) (co (cv x4) (cv x5) cplq)) (λ x5 . cv x2)) (λ x4 . cv x1)))) ⟶ wceq cmp (cmpt2 (λ x1 x2 . cnp) (λ x1 x2 . cnp) (λ x1 x2 . cab (λ x3 . wrex (λ x4 . wrex (λ x5 . wceq (cv x3) (co (cv x4) (cv x5) cmq)) (λ x5 . cv x2)) (λ x4 . cv x1)))) ⟶ wceq cltp (copab (λ x1 x2 . wa (wa (wcel (cv x1) cnp) (wcel (cv x2) cnp)) (wpss (cv x1) (cv x2)))) ⟶ wceq cer (copab (λ x1 x2 . wa (wa (wcel (cv x1) (cxp cnp cnp)) (wcel (cv x2) (cxp cnp cnp))) (wex (λ x3 . wex (λ x4 . wex (λ x5 . wex (λ x6 . wa (wa (wceq (cv x1) (cop (cv x3) (cv x4))) (wceq (cv x2) (cop (cv x5) (cv x6)))) (wceq (co (cv x3) (cv x6) cpp) (co (cv x4) (cv x5) cpp))))))))) ⟶ wceq cnr (cqs (cxp cnp cnp) cer) ⟶ wceq cplr (coprab (λ x1 x2 x3 . wa (wa (wcel (cv x1) cnr) (wcel (cv x2) cnr)) (wex (λ x4 . wex (λ x5 . wex (λ x6 . wex (λ x7 . wa (wa (wceq (cv x1) (cec (cop (cv x4) (cv x5)) cer)) (wceq (cv x2) (cec (cop (cv x6) (cv x7)) cer))) (wceq (cv x3) (cec (cop (co (cv x4) (cv x6) cpp) (co (cv x5) (cv x7) cpp)) cer))))))))) ⟶ x0) ⟶ x0
Axiom df_mr__df_ltr__df_0r__df_1r__df_m1r__df_c__df_0__df_1__df_i__df_r__df_add__df_mul__df_lt__df_pnf__df_mnf__df_xr__df_ltxr__df_le : ∀ x0 : ο . (wceq cmr (coprab (λ x1 x2 x3 . wa (wa (wcel (cv x1) cnr) (wcel (cv x2) cnr)) (wex (λ x4 . wex (λ x5 . wex (λ x6 . wex (λ x7 . wa (wa (wceq (cv x1) (cec (cop (cv x4) (cv x5)) cer)) (wceq (cv x2) (cec (cop (cv x6) (cv x7)) cer))) (wceq (cv x3) (cec (cop (co (co (cv x4) (cv x6) cmp) (co (cv x5) (cv x7) cmp) cpp) (co (co (cv x4) (cv x7) cmp) (co (cv x5) (cv x6) cmp) cpp)) cer))))))))) ⟶ wceq cltr (copab (λ x1 x2 . wa (wa (wcel (cv x1) cnr) (wcel (cv x2) cnr)) (wex (λ x3 . wex (λ x4 . wex (λ x5 . wex (λ x6 . wa (wa (wceq (cv x1) (cec (cop (cv x3) (cv x4)) cer)) (wceq (cv x2) (cec (cop (cv x5) (cv x6)) cer))) (wbr (co (cv x3) (cv x6) cpp) (co (cv x4) (cv x5) cpp) cltp)))))))) ⟶ wceq c0r (cec (cop c1p c1p) cer) ⟶ wceq c1r (cec (cop (co c1p c1p cpp) c1p) cer) ⟶ wceq cm1r (cec (cop c1p (co c1p c1p cpp)) cer) ⟶ wceq cc (cxp cnr cnr) ⟶ wceq cc0 (cop c0r c0r) ⟶ wceq c1 (cop c1r c0r) ⟶ wceq ci (cop c0r c1r) ⟶ wceq cr (cxp cnr (csn c0r)) ⟶ wceq caddc (coprab (λ x1 x2 x3 . wa (wa (wcel (cv x1) cc) (wcel (cv x2) cc)) (wex (λ x4 . wex (λ x5 . wex (λ x6 . wex (λ x7 . wa (wa (wceq (cv x1) (cop (cv x4) (cv x5))) (wceq (cv x2) (cop (cv x6) (cv x7)))) (wceq (cv x3) (cop (co (cv x4) (cv x6) cplr) (co (cv x5) (cv x7) cplr)))))))))) ⟶ wceq cmul (coprab (λ x1 x2 x3 . wa (wa (wcel (cv x1) cc) (wcel (cv x2) cc)) (wex (λ x4 . wex (λ x5 . wex (λ x6 . wex (λ x7 . wa (wa (wceq (cv x1) (cop (cv x4) (cv x5))) (wceq (cv x2) (cop (cv x6) (cv x7)))) (wceq (cv x3) (cop (co (co (cv x4) (cv x6) cmr) (co cm1r (co (cv x5) (cv x7) cmr) cmr) cplr) (co (co (cv x5) (cv x6) cmr) (co (cv x4) (cv x7) cmr) cplr)))))))))) ⟶ wceq cltrr (copab (λ x1 x2 . wa (wa (wcel (cv x1) cr) (wcel (cv x2) cr)) (wex (λ x3 . wex (λ x4 . wa (wa (wceq (cv x1) (cop (cv x3) c0r)) (wceq (cv x2) (cop (cv x4) c0r))) (wbr (cv x3) (cv x4) cltr)))))) ⟶ wceq cpnf (cpw (cuni cc)) ⟶ wceq cmnf (cpw cpnf) ⟶ wceq cxr (cun cr (cpr cpnf cmnf)) ⟶ wceq clt (cun (copab (λ x1 x2 . w3a (wcel (cv x1) cr) (wcel (cv x2) cr) (wbr (cv x1) (cv x2) cltrr))) (cun (cxp (cun cr (csn cmnf)) (csn cpnf)) (cxp (csn cmnf) cr))) ⟶ wceq cle (cdif (cxp cxr cxr) (ccnv clt)) ⟶ x0) ⟶ x0
Axiom df_sub__df_neg__df_div__df_nn__df_2__df_3__df_4__df_5__df_6__df_7__df_8__df_9__df_10OLD__df_n0__df_xnn0__df_z__df_dec__df_uz : ∀ x0 : ο . (wceq cmin (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cc) (λ x1 x2 . crio (λ x3 . wceq (co (cv x2) (cv x3) caddc) (cv x1)) (λ x3 . cc))) ⟶ (∀ x1 : ι → ο . wceq (cneg x1) (co cc0 x1 cmin)) ⟶ wceq cdiv (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cdif cc (csn cc0)) (λ x1 x2 . crio (λ x3 . wceq (co (cv x2) (cv x3) cmul) (cv x1)) (λ x3 . cc))) ⟶ wceq cn (cima (crdg (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) c1 caddc)) c1) com) ⟶ wceq c2 (co c1 c1 caddc) ⟶ wceq c3 (co c2 c1 caddc) ⟶ wceq c4 (co c3 c1 caddc) ⟶ wceq c5 (co c4 c1 caddc) ⟶ wceq c6 (co c5 c1 caddc) ⟶ wceq c7 (co c6 c1 caddc) ⟶ wceq c8 (co c7 c1 caddc) ⟶ wceq c9 (co c8 c1 caddc) ⟶ wceq c10 (co c9 c1 caddc) ⟶ wceq cn0 (cun cn (csn cc0)) ⟶ wceq cxnn0 (cun cn0 (csn cpnf)) ⟶ wceq cz (crab (λ x1 . w3o (wceq (cv x1) cc0) (wcel (cv x1) cn) (wcel (cneg (cv x1)) cn)) (λ x1 . cr)) ⟶ (∀ x1 x2 : ι → ο . wceq (cdc x1 x2) (co (co (co c9 c1 caddc) x1 cmul) x2 caddc)) ⟶ wceq cuz (cmpt (λ x1 . cz) (λ x1 . crab (λ x2 . wbr (cv x1) (cv x2) cle) (λ x2 . cz))) ⟶ x0) ⟶ x0
Axiom df_q__df_rp__df_xneg__df_xadd__df_xmul__df_ioo__df_ioc__df_ico__df_icc__df_fz__df_fzo__df_fl__df_ceil__df_mod__df_seq__df_exp__df_fac__df_bc : ∀ x0 : ο . (wceq cq (cima cdiv (cxp cz cn)) ⟶ wceq crp (crab (λ x1 . wbr cc0 (cv x1) clt) (λ x1 . cr)) ⟶ (∀ x1 : ι → ο . wceq (cxne x1) (cif (wceq x1 cpnf) cmnf (cif (wceq x1 cmnf) cpnf (cneg x1)))) ⟶ wceq cxad (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . cif (wceq (cv x1) cpnf) (cif (wceq (cv x2) cmnf) cc0 cpnf) (cif (wceq (cv x1) cmnf) (cif (wceq (cv x2) cpnf) cc0 cmnf) (cif (wceq (cv x2) cpnf) cpnf (cif (wceq (cv x2) cmnf) cmnf (co (cv x1) (cv x2) caddc)))))) ⟶ wceq cxmu (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . cif (wo (wceq (cv x1) cc0) (wceq (cv x2) cc0)) cc0 (cif (wo (wo (wa (wbr cc0 (cv x2) clt) (wceq (cv x1) cpnf)) (wa (wbr (cv x2) cc0 clt) (wceq (cv x1) cmnf))) (wo (wa (wbr cc0 (cv x1) clt) (wceq (cv x2) cpnf)) (wa (wbr (cv x1) cc0 clt) (wceq (cv x2) cmnf)))) cpnf (cif (wo (wo (wa (wbr cc0 (cv x2) clt) (wceq (cv x1) cmnf)) (wa (wbr (cv x2) cc0 clt) (wceq (cv x1) cpnf))) (wo (wa (wbr cc0 (cv x1) clt) (wceq (cv x2) cmnf)) (wa (wbr (cv x1) cc0 clt) (wceq (cv x2) cpnf)))) cmnf (co (cv x1) (cv x2) cmul))))) ⟶ wceq cioo (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . crab (λ x3 . wa (wbr (cv x1) (cv x3) clt) (wbr (cv x3) (cv x2) clt)) (λ x3 . cxr))) ⟶ wceq cioc (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . crab (λ x3 . wa (wbr (cv x1) (cv x3) clt) (wbr (cv x3) (cv x2) cle)) (λ x3 . cxr))) ⟶ wceq cico (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . crab (λ x3 . wa (wbr (cv x1) (cv x3) cle) (wbr (cv x3) (cv x2) clt)) (λ x3 . cxr))) ⟶ wceq cicc (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . crab (λ x3 . wa (wbr (cv x1) (cv x3) cle) (wbr (cv x3) (cv x2) cle)) (λ x3 . cxr))) ⟶ wceq cfz (cmpt2 (λ x1 x2 . cz) (λ x1 x2 . cz) (λ x1 x2 . crab (λ x3 . wa (wbr (cv x1) (cv x3) cle) (wbr (cv x3) (cv x2) cle)) (λ x3 . cz))) ⟶ wceq cfzo (cmpt2 (λ x1 x2 . cz) (λ x1 x2 . cz) (λ x1 x2 . co (cv x1) (co (cv x2) c1 cmin) cfz)) ⟶ wceq cfl (cmpt (λ x1 . cr) (λ x1 . crio (λ x2 . wa (wbr (cv x2) (cv x1) cle) (wbr (cv x1) (co (cv x2) c1 caddc) clt)) (λ x2 . cz))) ⟶ wceq cceil (cmpt (λ x1 . cr) (λ x1 . cneg (cfv (cneg (cv x1)) cfl))) ⟶ wceq cmo (cmpt2 (λ x1 x2 . cr) (λ x1 x2 . crp) (λ x1 x2 . co (cv x1) (co (cv x2) (cfv (co (cv x1) (cv x2) cdiv) cfl) cmul) cmin)) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cseq x1 x2 x3) (cima (crdg (cmpt2 (λ x4 x5 . cvv) (λ x4 x5 . cvv) (λ x4 x5 . cop (co (cv x4) c1 caddc) (co (cv x5) (cfv (co (cv x4) c1 caddc) x2) x1))) (cop x3 (cfv x3 x2))) com)) ⟶ wceq cexp (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cz) (λ x1 x2 . cif (wceq (cv x2) cc0) c1 (cif (wbr cc0 (cv x2) clt) (cfv (cv x2) (cseq cmul (cxp cn (csn (cv x1))) c1)) (co c1 (cfv (cneg (cv x2)) (cseq cmul (cxp cn (csn (cv x1))) c1)) cdiv)))) ⟶ wceq cfa (cun (csn (cop cc0 c1)) (cseq cmul cid c1)) ⟶ wceq cbc (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cz) (λ x1 x2 . cif (wcel (cv x2) (co cc0 (cv x1) cfz)) (co (cfv (cv x1) cfa) (co (cfv (co (cv x1) (cv x2) cmin) cfa) (cfv (cv x2) cfa) cmul) cdiv) cc0)) ⟶ x0) ⟶ x0
Axiom df_hash__df_word__df_lsw__df_concat__df_s1__df_substr__df_splice__df_reverse__df_reps__df_csh__df_s2__df_s3__df_s4__df_s5__df_s6__df_s7__df_s8__df_trcl : ∀ x0 : ο . (wceq chash (cun (ccom (cres (crdg (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) c1 caddc)) cc0) com) ccrd) (cxp (cdif cvv cfn) (csn cpnf))) ⟶ (∀ x1 : ι → ο . wceq (cword x1) (cab (λ x2 . wrex (λ x3 . wf (co cc0 (cv x3) cfzo) x1 (cv x2)) (λ x3 . cn0)))) ⟶ wceq clsw (cmpt (λ x1 . cvv) (λ x1 . cfv (co (cfv (cv x1) chash) c1 cmin) (cv x1))) ⟶ wceq cconcat (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . co cc0 (co (cfv (cv x1) chash) (cfv (cv x2) chash) caddc) cfzo) (λ x3 . cif (wcel (cv x3) (co cc0 (cfv (cv x1) chash) cfzo)) (cfv (cv x3) (cv x1)) (cfv (co (cv x3) (cfv (cv x1) chash) cmin) (cv x2))))) ⟶ (∀ x1 : ι → ο . wceq (cs1 x1) (csn (cop cc0 (cfv x1 cid)))) ⟶ wceq csubstr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cxp cz cz) (λ x1 x2 . cif (wss (co (cfv (cv x2) c1st) (cfv (cv x2) c2nd) cfzo) (cdm (cv x1))) (cmpt (λ x3 . co cc0 (co (cfv (cv x2) c2nd) (cfv (cv x2) c1st) cmin) cfzo) (λ x3 . cfv (co (cv x3) (cfv (cv x2) c1st) caddc) (cv x1))) c0)) ⟶ wceq csplice (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (co (cv x1) (cop cc0 (cfv (cfv (cv x2) c1st) c1st)) csubstr) (cfv (cv x2) c2nd) cconcat) (co (cv x1) (cop (cfv (cfv (cv x2) c1st) c2nd) (cfv (cv x1) chash)) csubstr) cconcat)) ⟶ wceq creverse (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . co cc0 (cfv (cv x1) chash) cfzo) (λ x2 . cfv (co (co (cfv (cv x1) chash) c1 cmin) (cv x2) cmin) (cv x1)))) ⟶ wceq creps (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cn0) (λ x1 x2 . cmpt (λ x3 . co cc0 (cv x2) cfzo) (λ x3 . cv x1))) ⟶ wceq ccsh (cmpt2 (λ x1 x2 . cab (λ x3 . wrex (λ x4 . wfn (cv x3) (co cc0 (cv x4) cfzo)) (λ x4 . cn0))) (λ x1 x2 . cz) (λ x1 x2 . cif (wceq (cv x1) c0) c0 (co (co (cv x1) (cop (co (cv x2) (cfv (cv x1) chash) cmo) (cfv (cv x1) chash)) csubstr) (co (cv x1) (cop cc0 (co (cv x2) (cfv (cv x1) chash) cmo)) csubstr) cconcat))) ⟶ (∀ x1 x2 : ι → ο . wceq (cs2 x1 x2) (co (cs1 x1) (cs1 x2) cconcat)) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cs3 x1 x2 x3) (co (cs2 x1 x2) (cs1 x3) cconcat)) ⟶ (∀ x1 x2 x3 x4 : ι → ο . wceq (cs4 x1 x2 x3 x4) (co (cs3 x1 x2 x3) (cs1 x4) cconcat)) ⟶ (∀ x1 x2 x3 x4 x5 : ι → ο . wceq (cs5 x1 x2 x3 x4 x5) (co (cs4 x1 x2 x3 x4) (cs1 x5) cconcat)) ⟶ (∀ x1 x2 x3 x4 x5 x6 : ι → ο . wceq (cs6 x1 x2 x3 x4 x5 x6) (co (cs5 x1 x2 x3 x4 x5) (cs1 x6) cconcat)) ⟶ (∀ x1 x2 x3 x4 x5 x6 x7 : ι → ο . wceq (cs7 x1 x2 x3 x4 x5 x6 x7) (co (cs6 x1 x2 x3 x4 x5 x6) (cs1 x7) cconcat)) ⟶ (∀ x1 x2 x3 x4 x5 x6 x7 x8 : ι → ο . wceq (cs8 x1 x2 x3 x4 x5 x6 x7 x8) (co (cs7 x1 x2 x3 x4 x5 x6 x7) (cs1 x8) cconcat)) ⟶ wceq ctcl (cmpt (λ x1 . cvv) (λ x1 . cint (cab (λ x2 . wa (wss (cv x1) (cv x2)) (wss (ccom (cv x2) (cv x2)) (cv x2)))))) ⟶ x0) ⟶ x0
Axiom df_rtrcl__df_relexp__df_rtrclrec__df_shft__df_sgn__df_cj__df_re__df_im__df_sqrt__df_abs__df_limsup__df_clim__df_rlim__df_o1__df_lo1__df_sum__df_prod__df_risefac : ∀ x0 : ο . (wceq crtcl (cmpt (λ x1 . cvv) (λ x1 . cint (cab (λ x2 . w3a (wss (cres cid (cun (cdm (cv x1)) (crn (cv x1)))) (cv x2)) (wss (cv x1) (cv x2)) (wss (ccom (cv x2) (cv x2)) (cv x2)))))) ⟶ wceq crelexp (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cn0) (λ x1 x2 . cif (wceq (cv x2) cc0) (cres cid (cun (cdm (cv x1)) (crn (cv x1)))) (cfv (cv x2) (cseq (cmpt2 (λ x3 x4 . cvv) (λ x3 x4 . cvv) (λ x3 x4 . ccom (cv x3) (cv x1))) (cmpt (λ x3 . cvv) (λ x3 . cv x1)) c1)))) ⟶ wceq crtrcl (cmpt (λ x1 . cvv) (λ x1 . ciun (λ x2 . cn0) (λ x2 . co (cv x1) (cv x2) crelexp))) ⟶ wceq cshi (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cc) (λ x1 x2 . copab (λ x3 x4 . wa (wcel (cv x3) cc) (wbr (co (cv x3) (cv x2) cmin) (cv x4) (cv x1))))) ⟶ wceq csgn (cmpt (λ x1 . cxr) (λ x1 . cif (wceq (cv x1) cc0) cc0 (cif (wbr (cv x1) cc0 clt) (cneg c1) c1))) ⟶ wceq ccj (cmpt (λ x1 . cc) (λ x1 . crio (λ x2 . wa (wcel (co (cv x1) (cv x2) caddc) cr) (wcel (co ci (co (cv x1) (cv x2) cmin) cmul) cr)) (λ x2 . cc))) ⟶ wceq cre (cmpt (λ x1 . cc) (λ x1 . co (co (cv x1) (cfv (cv x1) ccj) caddc) c2 cdiv)) ⟶ wceq cim (cmpt (λ x1 . cc) (λ x1 . cfv (co (cv x1) ci cdiv) cre)) ⟶ wceq csqrt (cmpt (λ x1 . cc) (λ x1 . crio (λ x2 . w3a (wceq (co (cv x2) c2 cexp) (cv x1)) (wbr cc0 (cfv (cv x2) cre) cle) (wnel (co ci (cv x2) cmul) crp)) (λ x2 . cc))) ⟶ wceq cabs (cmpt (λ x1 . cc) (λ x1 . cfv (co (cv x1) (cfv (cv x1) ccj) cmul) csqrt)) ⟶ wceq clsp (cmpt (λ x1 . cvv) (λ x1 . cinf (crn (cmpt (λ x2 . cr) (λ x2 . csup (cin (cima (cv x1) (co (cv x2) cpnf cico)) cxr) cxr clt))) cxr clt)) ⟶ wceq cli (copab (λ x1 x2 . wa (wcel (cv x2) cc) (wral (λ x3 . wrex (λ x4 . wral (λ x5 . wa (wcel (cfv (cv x5) (cv x1)) cc) (wbr (cfv (co (cfv (cv x5) (cv x1)) (cv x2) cmin) cabs) (cv x3) clt)) (λ x5 . cfv (cv x4) cuz)) (λ x4 . cz)) (λ x3 . crp)))) ⟶ wceq crli (copab (λ x1 x2 . wa (wa (wcel (cv x1) (co cc cr cpm)) (wcel (cv x2) cc)) (wral (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cv x4) (cv x5) cle ⟶ wbr (cfv (co (cfv (cv x5) (cv x1)) (cv x2) cmin) cabs) (cv x3) clt) (λ x5 . cdm (cv x1))) (λ x4 . cr)) (λ x3 . crp)))) ⟶ wceq co1 (crab (λ x1 . wrex (λ x2 . wrex (λ x3 . wral (λ x4 . wbr (cfv (cfv (cv x4) (cv x1)) cabs) (cv x3) cle) (λ x4 . cin (cdm (cv x1)) (co (cv x2) cpnf cico))) (λ x3 . cr)) (λ x2 . cr)) (λ x1 . co cc cr cpm)) ⟶ wceq clo1 (crab (λ x1 . wrex (λ x2 . wrex (λ x3 . wral (λ x4 . wbr (cfv (cv x4) (cv x1)) (cv x3) cle) (λ x4 . cin (cdm (cv x1)) (co (cv x2) cpnf cico))) (λ x3 . cr)) (λ x2 . cr)) (λ x1 . co cr cr cpm)) ⟶ (∀ x1 x2 : ι → ι → ο . ∀ x3 . wceq (csu (x1 x3) x2) (cio (λ x4 . wo (wrex (λ x5 . wa (wss (x1 x3) (cfv (cv x5) cuz)) (wbr (cseq caddc (cmpt (λ x6 . cz) (λ x6 . cif (wcel (cv x6) (x1 x3)) (csb (cv x6) x2) cc0)) (cv x5)) (cv x4) cli)) (λ x5 . cz)) (wrex (λ x5 . wex (λ x6 . wa (wf1o (co c1 (cv x5) cfz) (x1 x3) (cv x6)) (wceq (cv x4) (cfv (cv x5) (cseq caddc (cmpt (λ x7 . cn) (λ x7 . csb (cfv (cv x7) (cv x6)) x2)) c1))))) (λ x5 . cn))))) ⟶ (∀ x1 x2 : ι → ι → ο . ∀ x3 . wceq (cprod x1 x2) (cio (λ x4 . wo (wrex (λ x5 . w3a (wss (x1 x3) (cfv (cv x5) cuz)) (wrex (λ x6 . wex (λ x7 . wa (wne (cv x7) cc0) (wbr (cseq cmul (cmpt (λ x8 . cz) (λ x8 . cif (wcel (cv x8) (x1 x8)) (x2 x8) c1)) (cv x6)) (cv x7) cli))) (λ x6 . cfv (cv x5) cuz)) (wbr (cseq cmul (cmpt (λ x6 . cz) (λ x6 . cif (wcel (cv x6) (x1 x6)) (x2 x6) c1)) (cv x5)) (cv x4) cli)) (λ x5 . cz)) (wrex (λ x5 . wex (λ x6 . wa (wf1o (co c1 (cv x5) cfz) (x1 x3) (cv x6)) (wceq (cv x4) (cfv (cv x5) (cseq cmul (cmpt (λ x7 . cn) (λ x7 . csb (cfv (cv x7) (cv x6)) x2)) c1))))) (λ x5 . cn))))) ⟶ wceq crisefac (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cn0) (λ x1 x2 . cprod (λ x3 . co cc0 (co (cv x2) c1 cmin) cfz) (λ x3 . co (cv x1) (cv x3) caddc))) ⟶ x0) ⟶ x0
Axiom df_fallfac__df_bpoly__df_ef__df_e__df_sin__df_cos__df_tan__df_pi__df_dvds__df_bits__df_sad__df_smu__df_gcd__df_lcm__df_lcmf__df_prm__df_numer__df_denom : ∀ x0 : ο . (wceq cfallfac (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cn0) (λ x1 x2 . cprod (λ x3 . co cc0 (co (cv x2) c1 cmin) cfz) (λ x3 . co (cv x1) (cv x3) cmin))) ⟶ wceq cbp (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cc) (λ x1 x2 . cfv (cv x1) (cwrecs cn0 clt (cmpt (λ x3 . cvv) (λ x3 . csb (cfv (cdm (cv x3)) chash) (λ x4 . co (co (cv x2) (cv x4) cexp) (csu (cdm (cv x3)) (λ x5 . co (co (cv x4) (cv x5) cbc) (co (cfv (cv x5) (cv x3)) (co (co (cv x4) (cv x5) cmin) c1 caddc) cdiv) cmul)) cmin)))))) ⟶ wceq ce (cmpt (λ x1 . cc) (λ x1 . csu cn0 (λ x2 . co (co (cv x1) (cv x2) cexp) (cfv (cv x2) cfa) cdiv))) ⟶ wceq ceu (cfv c1 ce) ⟶ wceq csin (cmpt (λ x1 . cc) (λ x1 . co (co (cfv (co ci (cv x1) cmul) ce) (cfv (co (cneg ci) (cv x1) cmul) ce) cmin) (co c2 ci cmul) cdiv)) ⟶ wceq ccos (cmpt (λ x1 . cc) (λ x1 . co (co (cfv (co ci (cv x1) cmul) ce) (cfv (co (cneg ci) (cv x1) cmul) ce) caddc) c2 cdiv)) ⟶ wceq ctan (cmpt (λ x1 . cima (ccnv ccos) (cdif cc (csn cc0))) (λ x1 . co (cfv (cv x1) csin) (cfv (cv x1) ccos) cdiv)) ⟶ wceq cpi (cinf (cin crp (cima (ccnv csin) (csn cc0))) cr clt) ⟶ wceq cdvds (copab (λ x1 x2 . wa (wa (wcel (cv x1) cz) (wcel (cv x2) cz)) (wrex (λ x3 . wceq (co (cv x3) (cv x1) cmul) (cv x2)) (λ x3 . cz)))) ⟶ wceq cbits (cmpt (λ x1 . cz) (λ x1 . crab (λ x2 . wn (wbr c2 (cfv (co (cv x1) (co c2 (cv x2) cexp) cdiv) cfl) cdvds)) (λ x2 . cn0))) ⟶ wceq csad (cmpt2 (λ x1 x2 . cpw cn0) (λ x1 x2 . cpw cn0) (λ x1 x2 . crab (λ x3 . whad (wcel (cv x3) (cv x1)) (wcel (cv x3) (cv x2)) (wcel c0 (cfv (cv x3) (cseq (cmpt2 (λ x4 x5 . c2o) (λ x4 x5 . cn0) (λ x4 x5 . cif (wcad (wcel (cv x5) (cv x1)) (wcel (cv x5) (cv x2)) (wcel c0 (cv x4))) c1o c0)) (cmpt (λ x4 . cn0) (λ x4 . cif (wceq (cv x4) cc0) c0 (co (cv x4) c1 cmin))) cc0)))) (λ x3 . cn0))) ⟶ wceq csmu (cmpt2 (λ x1 x2 . cpw cn0) (λ x1 x2 . cpw cn0) (λ x1 x2 . crab (λ x3 . wcel (cv x3) (cfv (co (cv x3) c1 caddc) (cseq (cmpt2 (λ x4 x5 . cpw cn0) (λ x4 x5 . cn0) (λ x4 x5 . co (cv x4) (crab (λ x6 . wa (wcel (cv x5) (cv x1)) (wcel (co (cv x6) (cv x5) cmin) (cv x2))) (λ x6 . cn0)) csad)) (cmpt (λ x4 . cn0) (λ x4 . cif (wceq (cv x4) cc0) c0 (co (cv x4) c1 cmin))) cc0))) (λ x3 . cn0))) ⟶ wceq cgcd (cmpt2 (λ x1 x2 . cz) (λ x1 x2 . cz) (λ x1 x2 . cif (wa (wceq (cv x1) cc0) (wceq (cv x2) cc0)) cc0 (csup (crab (λ x3 . wa (wbr (cv x3) (cv x1) cdvds) (wbr (cv x3) (cv x2) cdvds)) (λ x3 . cz)) cr clt))) ⟶ wceq clcm (cmpt2 (λ x1 x2 . cz) (λ x1 x2 . cz) (λ x1 x2 . cif (wo (wceq (cv x1) cc0) (wceq (cv x2) cc0)) cc0 (cinf (crab (λ x3 . wa (wbr (cv x1) (cv x3) cdvds) (wbr (cv x2) (cv x3) cdvds)) (λ x3 . cn)) cr clt))) ⟶ wceq clcmf (cmpt (λ x1 . cpw cz) (λ x1 . cif (wcel cc0 (cv x1)) cc0 (cinf (crab (λ x2 . wral (λ x3 . wbr (cv x3) (cv x2) cdvds) (λ x3 . cv x1)) (λ x2 . cn)) cr clt))) ⟶ wceq cprime (crab (λ x1 . wbr (crab (λ x2 . wbr (cv x2) (cv x1) cdvds) (λ x2 . cn)) c2o cen) (λ x1 . cn)) ⟶ wceq cnumer (cmpt (λ x1 . cq) (λ x1 . cfv (crio (λ x2 . wa (wceq (co (cfv (cv x2) c1st) (cfv (cv x2) c2nd) cgcd) c1) (wceq (cv x1) (co (cfv (cv x2) c1st) (cfv (cv x2) c2nd) cdiv))) (λ x2 . cxp cz cn)) c1st)) ⟶ wceq cdenom (cmpt (λ x1 . cq) (λ x1 . cfv (crio (λ x2 . wa (wceq (co (cfv (cv x2) c1st) (cfv (cv x2) c2nd) cgcd) c1) (wceq (cv x1) (co (cfv (cv x2) c1st) (cfv (cv x2) c2nd) cdiv))) (λ x2 . cxp cz cn)) c2nd)) ⟶ x0) ⟶ x0
Axiom df_odz__df_phi__df_pc__df_gz__df_vdwap__df_vdwmc__df_vdwpc__df_ram__df_prmo__df_struct__df_ndx__df_slot__df_base__df_sets__df_ress__df_plusg__df_mulr__df_starv : ∀ x0 : ο . (wceq codz (cmpt (λ x1 . cn) (λ x1 . cmpt (λ x2 . crab (λ x3 . wceq (co (cv x3) (cv x1) cgcd) c1) (λ x3 . cz)) (λ x2 . cinf (crab (λ x3 . wbr (cv x1) (co (co (cv x2) (cv x3) cexp) c1 cmin) cdvds) (λ x3 . cn)) cr clt))) ⟶ wceq cphi (cmpt (λ x1 . cn) (λ x1 . cfv (crab (λ x2 . wceq (co (cv x2) (cv x1) cgcd) c1) (λ x2 . co c1 (cv x1) cfz)) chash)) ⟶ wceq cpc (cmpt2 (λ x1 x2 . cprime) (λ x1 x2 . cq) (λ x1 x2 . cif (wceq (cv x2) cc0) cpnf (cio (λ x3 . wrex (λ x4 . wrex (λ x5 . wa (wceq (cv x2) (co (cv x4) (cv x5) cdiv)) (wceq (cv x3) (co (csup (crab (λ x6 . wbr (co (cv x1) (cv x6) cexp) (cv x4) cdvds) (λ x6 . cn0)) cr clt) (csup (crab (λ x6 . wbr (co (cv x1) (cv x6) cexp) (cv x5) cdvds) (λ x6 . cn0)) cr clt) cmin))) (λ x5 . cn)) (λ x4 . cz))))) ⟶ wceq cgz (crab (λ x1 . wa (wcel (cfv (cv x1) cre) cz) (wcel (cfv (cv x1) cim) cz)) (λ x1 . cc)) ⟶ wceq cvdwa (cmpt (λ x1 . cn0) (λ x1 . cmpt2 (λ x2 x3 . cn) (λ x2 x3 . cn) (λ x2 x3 . crn (cmpt (λ x4 . co cc0 (co (cv x1) c1 cmin) cfz) (λ x4 . co (cv x2) (co (cv x4) (cv x3) cmul) caddc))))) ⟶ wceq cvdwm (copab (λ x1 x2 . wex (λ x3 . wne (cin (crn (cfv (cv x1) cvdwa)) (cpw (cima (ccnv (cv x2)) (csn (cv x3))))) c0))) ⟶ wceq cvdwp (coprab (λ x1 x2 x3 . wrex (λ x4 . wrex (λ x5 . wa (wral (λ x6 . wss (co (co (cv x4) (cfv (cv x6) (cv x5)) caddc) (cfv (cv x6) (cv x5)) (cfv (cv x2) cvdwa)) (cima (ccnv (cv x3)) (csn (cfv (co (cv x4) (cfv (cv x6) (cv x5)) caddc) (cv x3))))) (λ x6 . co c1 (cv x1) cfz)) (wceq (cfv (crn (cmpt (λ x6 . co c1 (cv x1) cfz) (λ x6 . cfv (co (cv x4) (cfv (cv x6) (cv x5)) caddc) (cv x3)))) chash) (cv x1))) (λ x5 . co cn (co c1 (cv x1) cfz) cmap)) (λ x4 . cn))) ⟶ wceq cram (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . cinf (crab (λ x3 . ∀ x4 . wbr (cv x3) (cfv (cv x4) chash) cle ⟶ wral (λ x5 . wrex (λ x6 . wrex (λ x7 . wa (wbr (cfv (cv x6) (cv x2)) (cfv (cv x7) chash) cle) (wral (λ x8 . wceq (cfv (cv x8) chash) (cv x1) ⟶ wceq (cfv (cv x8) (cv x5)) (cv x6)) (λ x8 . cpw (cv x7)))) (λ x7 . cpw (cv x4))) (λ x6 . cdm (cv x2))) (λ x5 . co (cdm (cv x2)) (crab (λ x6 . wceq (cfv (cv x6) chash) (cv x1)) (λ x6 . cpw (cv x4))) cmap)) (λ x3 . cn0)) cxr clt)) ⟶ wceq cprmo (cmpt (λ x1 . cn0) (λ x1 . cprod (λ x2 . co c1 (cv x1) cfz) (λ x2 . cif (wcel (cv x2) cprime) (cv x2) c1))) ⟶ wceq cstr (copab (λ x1 x2 . w3a (wcel (cv x2) (cin cle (cxp cn cn))) (wfun (cdif (cv x1) (csn c0))) (wss (cdm (cv x1)) (cfv (cv x2) cfz)))) ⟶ wceq cnx (cres cid cn) ⟶ (∀ x1 : ι → ο . wceq (cslot x1) (cmpt (λ x2 . cvv) (λ x2 . cfv x1 (cv x2)))) ⟶ wceq cbs (cslot c1) ⟶ wceq csts (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cun (cres (cv x1) (cdif cvv (cdm (csn (cv x2))))) (csn (cv x2)))) ⟶ wceq cress (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cif (wss (cfv (cv x1) cbs) (cv x2)) (cv x1) (co (cv x1) (cop (cfv cnx cbs) (cin (cv x2) (cfv (cv x1) cbs))) csts))) ⟶ wceq cplusg (cslot c2) ⟶ wceq cmulr (cslot c3) ⟶ wceq cstv (cslot c4) ⟶ x0) ⟶ x0
Axiom df_sca__df_vsca__df_ip__df_tset__df_ple__df_ocomp__df_ds__df_unif__df_hom__df_cco__df_rest__df_topn__df_0g__df_gsum__df_topgen__df_pt__df_prds__df_pws : ∀ x0 : ο . (wceq csca (cslot c5) ⟶ wceq cvsca (cslot c6) ⟶ wceq cip (cslot c8) ⟶ wceq cts (cslot c9) ⟶ wceq cple (cslot (cdc c1 cc0)) ⟶ wceq coc (cslot (cdc c1 c1)) ⟶ wceq cds (cslot (cdc c1 c2)) ⟶ wceq cunif (cslot (cdc c1 c3)) ⟶ wceq chom (cslot (cdc c1 c4)) ⟶ wceq cco (cslot (cdc c1 c5)) ⟶ wceq crest (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crn (cmpt (λ x3 . cv x1) (λ x3 . cin (cv x3) (cv x2))))) ⟶ wceq ctopn (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cv x1) cts) (cfv (cv x1) cbs) crest)) ⟶ wceq c0g (cmpt (λ x1 . cvv) (λ x1 . cio (λ x2 . wa (wcel (cv x2) (cfv (cv x1) cbs)) (wral (λ x3 . wa (wceq (co (cv x2) (cv x3) (cfv (cv x1) cplusg)) (cv x3)) (wceq (co (cv x3) (cv x2) (cfv (cv x1) cplusg)) (cv x3))) (λ x3 . cfv (cv x1) cbs))))) ⟶ wceq cgsu (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (crab (λ x3 . wral (λ x4 . wa (wceq (co (cv x3) (cv x4) (cfv (cv x1) cplusg)) (cv x4)) (wceq (co (cv x4) (cv x3) (cfv (cv x1) cplusg)) (cv x4))) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) cbs)) (λ x3 . cif (wss (crn (cv x2)) (cv x3)) (cfv (cv x1) c0g) (cif (wcel (cdm (cv x2)) (crn cfz)) (cio (λ x4 . wex (λ x5 . wrex (λ x6 . wa (wceq (cdm (cv x2)) (co (cv x5) (cv x6) cfz)) (wceq (cv x4) (cfv (cv x6) (cseq (cfv (cv x1) cplusg) (cv x2) (cv x5))))) (λ x6 . cfv (cv x5) cuz)))) (cio (λ x4 . wex (λ x5 . wsbc (λ x6 . wa (wf1o (co c1 (cfv (cv x6) chash) cfz) (cv x6) (cv x5)) (wceq (cv x4) (cfv (cfv (cv x6) chash) (cseq (cfv (cv x1) cplusg) (ccom (cv x2) (cv x5)) c1)))) (cima (ccnv (cv x2)) (cdif cvv (cv x3)))))))))) ⟶ wceq ctg (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wss (cv x2) (cuni (cin (cv x1) (cpw (cv x2))))))) ⟶ wceq cpt (cmpt (λ x1 . cvv) (λ x1 . cfv (cab (λ x2 . wex (λ x3 . wa (w3a (wfn (cv x3) (cdm (cv x1))) (wral (λ x4 . wcel (cfv (cv x4) (cv x3)) (cfv (cv x4) (cv x1))) (λ x4 . cdm (cv x1))) (wrex (λ x4 . wral (λ x5 . wceq (cfv (cv x5) (cv x3)) (cuni (cfv (cv x5) (cv x1)))) (λ x5 . cdif (cdm (cv x1)) (cv x4))) (λ x4 . cfn))) (wceq (cv x2) (cixp (λ x4 . cdm (cv x1)) (λ x4 . cfv (cv x4) (cv x3))))))) ctg)) ⟶ wceq cprds (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cixp (λ x3 . cdm (cv x2)) (λ x3 . cfv (cfv (cv x3) (cv x2)) cbs)) (λ x3 . csb (cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . cixp (λ x6 . cdm (cv x2)) (λ x6 . co (cfv (cv x6) (cv x4)) (cfv (cv x6) (cv x5)) (cfv (cfv (cv x6) (cv x2)) chom)))) (λ x4 . cun (cun (ctp (cop (cfv cnx cbs) (cv x3)) (cop (cfv cnx cplusg) (cmpt2 (λ x5 x6 . cv x3) (λ x5 x6 . cv x3) (λ x5 x6 . cmpt (λ x7 . cdm (cv x2)) (λ x7 . co (cfv (cv x7) (cv x5)) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cplusg))))) (cop (cfv cnx cmulr) (cmpt2 (λ x5 x6 . cv x3) (λ x5 x6 . cv x3) (λ x5 x6 . cmpt (λ x7 . cdm (cv x2)) (λ x7 . co (cfv (cv x7) (cv x5)) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cmulr)))))) (ctp (cop (cfv cnx csca) (cv x1)) (cop (cfv cnx cvsca) (cmpt2 (λ x5 x6 . cfv (cv x1) cbs) (λ x5 x6 . cv x3) (λ x5 x6 . cmpt (λ x7 . cdm (cv x2)) (λ x7 . co (cv x5) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cvsca))))) (cop (cfv cnx cip) (cmpt2 (λ x5 x6 . cv x3) (λ x5 x6 . cv x3) (λ x5 x6 . co (cv x1) (cmpt (λ x7 . cdm (cv x2)) (λ x7 . co (cfv (cv x7) (cv x5)) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cip))) cgsu))))) (cun (ctp (cop (cfv cnx cts) (cfv (ccom ctopn (cv x2)) cpt)) (cop (cfv cnx cple) (copab (λ x5 x6 . wa (wss (cpr (cv x5) (cv x6)) (cv x3)) (wral (λ x7 . wbr (cfv (cv x7) (cv x5)) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cple)) (λ x7 . cdm (cv x2)))))) (cop (cfv cnx cds) (cmpt2 (λ x5 x6 . cv x3) (λ x5 x6 . cv x3) (λ x5 x6 . csup (cun (crn (cmpt (λ x7 . cdm (cv x2)) (λ x7 . co (cfv (cv x7) (cv x5)) (cfv (cv x7) (cv x6)) (cfv (cfv (cv x7) (cv x2)) cds)))) (csn cc0)) cxr clt)))) (cpr (cop (cfv cnx chom) (cv x4)) (cop (cfv cnx cco) (cmpt2 (λ x5 x6 . cxp (cv x3) (cv x3)) (λ x5 x6 . cv x3) (λ x5 x6 . cmpt2 (λ x7 x8 . co (cv x6) (cfv (cv x5) c2nd) (cv x4)) (λ x7 x8 . cfv (cv x5) (cv x4)) (λ x7 x8 . cmpt (λ x9 . cdm (cv x2)) (λ x9 . co (cfv (cv x9) (cv x7)) (cfv (cv x9) (cv x8)) (co (cop (cfv (cv x9) (cfv (cv x5) c1st)) (cfv (cv x9) (cfv (cv x5) c2nd))) (cfv (cv x9) (cv x6)) (cfv (cfv (cv x9) (cv x2)) cco))))))))))))) ⟶ wceq cpws (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cfv (cv x1) csca) (cxp (cv x2) (csn (cv x1))) cprds)) ⟶ x0) ⟶ x0
Axiom df_ordt__df_xrs__df_qtop__df_imas__df_qus__df_xps__df_mre__df_mrc__df_mri__df_acs__df_cat__df_cid__df_homf__df_comf__df_oppc__df_mon__df_epi__df_sect : ∀ x0 : ο . (wceq cordt (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cun (csn (cdm (cv x1))) (crn (cun (cmpt (λ x2 . cdm (cv x1)) (λ x2 . crab (λ x3 . wn (wbr (cv x3) (cv x2) (cv x1))) (λ x3 . cdm (cv x1)))) (cmpt (λ x2 . cdm (cv x1)) (λ x2 . crab (λ x3 . wn (wbr (cv x2) (cv x3) (cv x1))) (λ x3 . cdm (cv x1))))))) cfi) ctg)) ⟶ wceq cxrs (cun (ctp (cop (cfv cnx cbs) cxr) (cop (cfv cnx cplusg) cxad) (cop (cfv cnx cmulr) cxmu)) (ctp (cop (cfv cnx cts) (cfv cle cordt)) (cop (cfv cnx cple) cle) (cop (cfv cnx cds) (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cxr) (λ x1 x2 . cif (wbr (cv x1) (cv x2) cle) (co (cv x2) (cxne (cv x1)) cxad) (co (cv x1) (cxne (cv x2)) cxad)))))) ⟶ wceq cqtop (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wcel (cin (cima (ccnv (cv x2)) (cv x3)) (cuni (cv x1))) (cv x1)) (λ x3 . cpw (cima (cv x2) (cuni (cv x1)))))) ⟶ wceq cimas (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x2) cbs) (λ x3 . cun (cun (ctp (cop (cfv cnx cbs) (crn (cv x1))) (cop (cfv cnx cplusg) (ciun (λ x4 . cv x3) (λ x4 . ciun (λ x5 . cv x3) (λ x5 . csn (cop (cop (cfv (cv x4) (cv x1)) (cfv (cv x5) (cv x1))) (cfv (co (cv x4) (cv x5) (cfv (cv x2) cplusg)) (cv x1))))))) (cop (cfv cnx cmulr) (ciun (λ x4 . cv x3) (λ x4 . ciun (λ x5 . cv x3) (λ x5 . csn (cop (cop (cfv (cv x4) (cv x1)) (cfv (cv x5) (cv x1))) (cfv (co (cv x4) (cv x5) (cfv (cv x2) cmulr)) (cv x1)))))))) (ctp (cop (cfv cnx csca) (cfv (cv x2) csca)) (cop (cfv cnx cvsca) (ciun (λ x4 . cv x3) (λ x4 . cmpt2 (λ x5 x6 . cfv (cfv (cv x2) csca) cbs) (λ x5 x6 . csn (cfv (cv x4) (cv x1))) (λ x5 x6 . cfv (co (cv x5) (cv x4) (cfv (cv x2) cvsca)) (cv x1))))) (cop (cfv cnx cip) (ciun (λ x4 . cv x3) (λ x4 . ciun (λ x5 . cv x3) (λ x5 . csn (cop (cop (cfv (cv x4) (cv x1)) (cfv (cv x5) (cv x1))) (co (cv x4) (cv x5) (cfv (cv x2) cip))))))))) (ctp (cop (cfv cnx cts) (co (cfv (cv x2) ctopn) (cv x1) cqtop)) (cop (cfv cnx cple) (ccom (ccom (cv x1) (cfv (cv x2) cple)) (ccnv (cv x1)))) (cop (cfv cnx cds) (cmpt2 (λ x4 x5 . crn (cv x1)) (λ x4 x5 . crn (cv x1)) (λ x4 x5 . cinf (ciun (λ x6 . cn) (λ x6 . crn (cmpt (λ x7 . crab (λ x8 . w3a (wceq (cfv (cfv (cfv c1 (cv x8)) c1st) (cv x1)) (cv x4)) (wceq (cfv (cfv (cfv (cv x6) (cv x8)) c2nd) (cv x1)) (cv x5)) (wral (λ x9 . wceq (cfv (cfv (cfv (cv x9) (cv x8)) c2nd) (cv x1)) (cfv (cfv (cfv (co (cv x9) c1 caddc) (cv x8)) c1st) (cv x1))) (λ x9 . co c1 (co (cv x6) c1 cmin) cfz))) (λ x8 . co (cxp (cv x3) (cv x3)) (co c1 (cv x6) cfz) cmap)) (λ x7 . co cxrs (ccom (cfv (cv x2) cds) (cv x7)) cgsu)))) cxr clt))))))) ⟶ wceq cqus (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cmpt (λ x3 . cfv (cv x1) cbs) (λ x3 . cec (cv x3) (cv x2))) (cv x1) cimas)) ⟶ wceq cxps (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (ccnv (cmpt2 (λ x3 x4 . cfv (cv x1) cbs) (λ x3 x4 . cfv (cv x2) cbs) (λ x3 x4 . ccnv (co (csn (cv x3)) (csn (cv x4)) ccda)))) (co (cfv (cv x1) csca) (ccnv (co (csn (cv x1)) (csn (cv x2)) ccda)) cprds) cimas)) ⟶ wceq cmre (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wcel (cv x1) (cv x2)) (wral (λ x3 . wne (cv x3) c0 ⟶ wcel (cint (cv x3)) (cv x2)) (λ x3 . cpw (cv x2)))) (λ x2 . cpw (cpw (cv x1))))) ⟶ wceq cmrc (cmpt (λ x1 . cuni (crn cmre)) (λ x1 . cmpt (λ x2 . cpw (cuni (cv x1))) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cv x1))))) ⟶ wceq cmri (cmpt (λ x1 . cuni (crn cmre)) (λ x1 . crab (λ x2 . wral (λ x3 . wn (wcel (cv x3) (cfv (cdif (cv x2) (csn (cv x3))) (cfv (cv x1) cmrc)))) (λ x3 . cv x2)) (λ x2 . cpw (cuni (cv x1))))) ⟶ wceq cacs (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wex (λ x3 . wa (wf (cpw (cv x1)) (cpw (cv x1)) (cv x3)) (wral (λ x4 . wb (wcel (cv x4) (cv x2)) (wss (cuni (cima (cv x3) (cin (cpw (cv x4)) cfn))) (cv x4))) (λ x4 . cpw (cv x1))))) (λ x2 . cfv (cv x1) cmre))) ⟶ wceq ccat (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wral (λ x5 . wa (wrex (λ x6 . wral (λ x7 . wa (wral (λ x8 . wceq (co (cv x6) (cv x8) (co (cop (cv x7) (cv x5)) (cv x5) (cv x4))) (cv x8)) (λ x8 . co (cv x7) (cv x5) (cv x3))) (wral (λ x8 . wceq (co (cv x8) (cv x6) (co (cop (cv x5) (cv x5)) (cv x7) (cv x4))) (cv x8)) (λ x8 . co (cv x5) (cv x7) (cv x3)))) (λ x7 . cv x2)) (λ x6 . co (cv x5) (cv x5) (cv x3))) (wral (λ x6 . wral (λ x7 . wral (λ x8 . wral (λ x9 . wa (wcel (co (cv x9) (cv x8) (co (cop (cv x5) (cv x6)) (cv x7) (cv x4))) (co (cv x5) (cv x7) (cv x3))) (wral (λ x10 . wral (λ x11 . wceq (co (co (cv x11) (cv x9) (co (cop (cv x6) (cv x7)) (cv x10) (cv x4))) (cv x8) (co (cop (cv x5) (cv x6)) (cv x10) (cv x4))) (co (cv x11) (co (cv x9) (cv x8) (co (cop (cv x5) (cv x6)) (cv x7) (cv x4))) (co (cop (cv x5) (cv x7)) (cv x10) (cv x4)))) (λ x11 . co (cv x7) (cv x10) (cv x3))) (λ x10 . cv x2))) (λ x9 . co (cv x6) (cv x7) (cv x3))) (λ x8 . co (cv x5) (cv x6) (cv x3))) (λ x7 . cv x2)) (λ x6 . cv x2))) (λ x5 . cv x2)) (cfv (cv x1) cco)) (cfv (cv x1) chom)) (cfv (cv x1) cbs))) ⟶ wceq ccid (cmpt (λ x1 . ccat) (λ x1 . csb (cfv (cv x1) cbs) (λ x2 . csb (cfv (cv x1) chom) (λ x3 . csb (cfv (cv x1) cco) (λ x4 . cmpt (λ x5 . cv x2) (λ x5 . crio (λ x6 . wral (λ x7 . wa (wral (λ x8 . wceq (co (cv x6) (cv x8) (co (cop (cv x7) (cv x5)) (cv x5) (cv x4))) (cv x8)) (λ x8 . co (cv x7) (cv x5) (cv x3))) (wral (λ x8 . wceq (co (cv x8) (cv x6) (co (cop (cv x5) (cv x5)) (cv x7) (cv x4))) (cv x8)) (λ x8 . co (cv x5) (cv x7) (cv x3)))) (λ x7 . cv x2)) (λ x6 . co (cv x5) (cv x5) (cv x3)))))))) ⟶ wceq chomf (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . co (cv x2) (cv x3) (cfv (cv x1) chom)))) ⟶ wceq ccomf (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs)) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cmpt2 (λ x4 x5 . co (cfv (cv x2) c2nd) (cv x3) (cfv (cv x1) chom)) (λ x4 x5 . cfv (cv x2) (cfv (cv x1) chom)) (λ x4 x5 . co (cv x4) (cv x5) (co (cv x2) (cv x3) (cfv (cv x1) cco)))))) ⟶ wceq coppc (cmpt (λ x1 . cvv) (λ x1 . co (co (cv x1) (cop (cfv cnx chom) (ctpos (cfv (cv x1) chom))) csts) (cop (cfv cnx cco) (cmpt2 (λ x2 x3 . cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs)) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . ctpos (co (cop (cv x3) (cfv (cv x2) c2nd)) (cfv (cv x2) c1st) (cfv (cv x1) cco))))) csts)) ⟶ wceq cmon (cmpt (λ x1 . ccat) (λ x1 . csb (cfv (cv x1) cbs) (λ x2 . csb (cfv (cv x1) chom) (λ x3 . cmpt2 (λ x4 x5 . cv x2) (λ x4 x5 . cv x2) (λ x4 x5 . crab (λ x6 . wral (λ x7 . wfun (ccnv (cmpt (λ x8 . co (cv x7) (cv x4) (cv x3)) (λ x8 . co (cv x6) (cv x8) (co (cop (cv x7) (cv x4)) (cv x5) (cfv (cv x1) cco)))))) (λ x7 . cv x2)) (λ x6 . co (cv x4) (cv x5) (cv x3))))))) ⟶ wceq cepi (cmpt (λ x1 . ccat) (λ x1 . ctpos (cfv (cfv (cv x1) coppc) cmon))) ⟶ wceq csect (cmpt (λ x1 . ccat) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . copab (λ x4 x5 . wsbc (λ x6 . wa (wa (wcel (cv x4) (co (cv x2) (cv x3) (cv x6))) (wcel (cv x5) (co (cv x3) (cv x2) (cv x6)))) (wceq (co (cv x5) (cv x4) (co (cop (cv x2) (cv x3)) (cv x2) (cfv (cv x1) cco))) (cfv (cv x2) (cfv (cv x1) ccid)))) (cfv (cv x1) chom))))) ⟶ x0) ⟶ x0
Axiom df_inv__df_iso__df_cic__df_ssc__df_resc__df_subc__df_func__df_idfu__df_cofu__df_resf__df_full__df_fth__df_nat__df_fuc__df_inito__df_termo__df_zeroo__df_doma : ∀ x0 : ο . (wceq cinv (cmpt (λ x1 . ccat) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cin (co (cv x2) (cv x3) (cfv (cv x1) csect)) (ccnv (co (cv x3) (cv x2) (cfv (cv x1) csect)))))) ⟶ wceq ciso (cmpt (λ x1 . ccat) (λ x1 . ccom (cmpt (λ x2 . cvv) (λ x2 . cdm (cv x2))) (cfv (cv x1) cinv))) ⟶ wceq ccic (cmpt (λ x1 . ccat) (λ x1 . co (cfv (cv x1) ciso) c0 csupp)) ⟶ wceq cssc (copab (λ x1 x2 . wex (λ x3 . wa (wfn (cv x2) (cxp (cv x3) (cv x3))) (wrex (λ x4 . wcel (cv x1) (cixp (λ x5 . cxp (cv x4) (cv x4)) (λ x5 . cpw (cfv (cv x5) (cv x2))))) (λ x4 . cpw (cv x3)))))) ⟶ wceq cresc (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cv x1) (cdm (cdm (cv x2))) cress) (cop (cfv cnx chom) (cv x2)) csts)) ⟶ wceq csubc (cmpt (λ x1 . ccat) (λ x1 . cab (λ x2 . wa (wbr (cv x2) (cfv (cv x1) chomf) cssc) (wsbc (λ x3 . wral (λ x4 . wa (wcel (cfv (cv x4) (cfv (cv x1) ccid)) (co (cv x4) (cv x4) (cv x2))) (wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . wcel (co (cv x8) (cv x7) (co (cop (cv x4) (cv x5)) (cv x6) (cfv (cv x1) cco))) (co (cv x4) (cv x6) (cv x2))) (λ x8 . co (cv x5) (cv x6) (cv x2))) (λ x7 . co (cv x4) (cv x5) (cv x2))) (λ x6 . cv x3)) (λ x5 . cv x3))) (λ x4 . cv x3)) (cdm (cdm (cv x2))))))) ⟶ wceq cfunc (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . copab (λ x3 x4 . wsbc (λ x5 . w3a (wf (cv x5) (cfv (cv x2) cbs) (cv x3)) (wcel (cv x4) (cixp (λ x6 . cxp (cv x5) (cv x5)) (λ x6 . co (co (cfv (cfv (cv x6) c1st) (cv x3)) (cfv (cfv (cv x6) c2nd) (cv x3)) (cfv (cv x2) chom)) (cfv (cv x6) (cfv (cv x1) chom)) cmap))) (wral (λ x6 . wa (wceq (cfv (cfv (cv x6) (cfv (cv x1) ccid)) (co (cv x6) (cv x6) (cv x4))) (cfv (cfv (cv x6) (cv x3)) (cfv (cv x2) ccid))) (wral (λ x7 . wral (λ x8 . wral (λ x9 . wral (λ x10 . wceq (cfv (co (cv x10) (cv x9) (co (cop (cv x6) (cv x7)) (cv x8) (cfv (cv x1) cco))) (co (cv x6) (cv x8) (cv x4))) (co (cfv (cv x10) (co (cv x7) (cv x8) (cv x4))) (cfv (cv x9) (co (cv x6) (cv x7) (cv x4))) (co (cop (cfv (cv x6) (cv x3)) (cfv (cv x7) (cv x3))) (cfv (cv x8) (cv x3)) (cfv (cv x2) cco)))) (λ x10 . co (cv x7) (cv x8) (cfv (cv x1) chom))) (λ x9 . co (cv x6) (cv x7) (cfv (cv x1) chom))) (λ x8 . cv x5)) (λ x7 . cv x5))) (λ x6 . cv x5))) (cfv (cv x1) cbs)))) ⟶ wceq cidfu (cmpt (λ x1 . ccat) (λ x1 . csb (cfv (cv x1) cbs) (λ x2 . cop (cres cid (cv x2)) (cmpt (λ x3 . cxp (cv x2) (cv x2)) (λ x3 . cres cid (cfv (cv x3) (cfv (cv x1) chom))))))) ⟶ wceq ccofu (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cop (ccom (cfv (cv x1) c1st) (cfv (cv x2) c1st)) (cmpt2 (λ x3 x4 . cdm (cdm (cfv (cv x2) c2nd))) (λ x3 x4 . cdm (cdm (cfv (cv x2) c2nd))) (λ x3 x4 . ccom (co (cfv (cv x3) (cfv (cv x2) c1st)) (cfv (cv x4) (cfv (cv x2) c1st)) (cfv (cv x1) c2nd)) (co (cv x3) (cv x4) (cfv (cv x2) c2nd)))))) ⟶ wceq cresf (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cop (cres (cfv (cv x1) c1st) (cdm (cdm (cv x2)))) (cmpt (λ x3 . cdm (cv x2)) (λ x3 . cres (cfv (cv x3) (cfv (cv x1) c2nd)) (cfv (cv x3) (cv x2)))))) ⟶ wceq cful (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . copab (λ x3 x4 . wa (wbr (cv x3) (cv x4) (co (cv x1) (cv x2) cfunc)) (wral (λ x5 . wral (λ x6 . wceq (crn (co (cv x5) (cv x6) (cv x4))) (co (cfv (cv x5) (cv x3)) (cfv (cv x6) (cv x3)) (cfv (cv x2) chom))) (λ x6 . cfv (cv x1) cbs)) (λ x5 . cfv (cv x1) cbs))))) ⟶ wceq cfth (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . copab (λ x3 x4 . wa (wbr (cv x3) (cv x4) (co (cv x1) (cv x2) cfunc)) (wral (λ x5 . wral (λ x6 . wfun (ccnv (co (cv x5) (cv x6) (cv x4)))) (λ x6 . cfv (cv x1) cbs)) (λ x5 . cfv (cv x1) cbs))))) ⟶ wceq cnat (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . cmpt2 (λ x3 x4 . co (cv x1) (cv x2) cfunc) (λ x3 x4 . co (cv x1) (cv x2) cfunc) (λ x3 x4 . csb (cfv (cv x3) c1st) (λ x5 . csb (cfv (cv x4) c1st) (λ x6 . crab (λ x7 . wral (λ x8 . wral (λ x9 . wral (λ x10 . wceq (co (cfv (cv x9) (cv x7)) (cfv (cv x10) (co (cv x8) (cv x9) (cfv (cv x3) c2nd))) (co (cop (cfv (cv x8) (cv x5)) (cfv (cv x9) (cv x5))) (cfv (cv x9) (cv x6)) (cfv (cv x2) cco))) (co (cfv (cv x10) (co (cv x8) (cv x9) (cfv (cv x4) c2nd))) (cfv (cv x8) (cv x7)) (co (cop (cfv (cv x8) (cv x5)) (cfv (cv x8) (cv x6))) (cfv (cv x9) (cv x6)) (cfv (cv x2) cco)))) (λ x10 . co (cv x8) (cv x9) (cfv (cv x1) chom))) (λ x9 . cfv (cv x1) cbs)) (λ x8 . cfv (cv x1) cbs)) (λ x7 . cixp (λ x8 . cfv (cv x1) cbs) (λ x8 . co (cfv (cv x8) (cv x5)) (cfv (cv x8) (cv x6)) (cfv (cv x2) chom)))))))) ⟶ wceq cfuc (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . ctp (cop (cfv cnx cbs) (co (cv x1) (cv x2) cfunc)) (cop (cfv cnx chom) (co (cv x1) (cv x2) cnat)) (cop (cfv cnx cco) (cmpt2 (λ x3 x4 . cxp (co (cv x1) (cv x2) cfunc) (co (cv x1) (cv x2) cfunc)) (λ x3 x4 . co (cv x1) (cv x2) cfunc) (λ x3 x4 . csb (cfv (cv x3) c1st) (λ x5 . csb (cfv (cv x3) c2nd) (λ x6 . cmpt2 (λ x7 x8 . co (cv x6) (cv x4) (co (cv x1) (cv x2) cnat)) (λ x7 x8 . co (cv x5) (cv x6) (co (cv x1) (cv x2) cnat)) (λ x7 x8 . cmpt (λ x9 . cfv (cv x1) cbs) (λ x9 . co (cfv (cv x9) (cv x7)) (cfv (cv x9) (cv x8)) (co (cop (cfv (cv x9) (cfv (cv x5) c1st)) (cfv (cv x9) (cfv (cv x6) c1st))) (cfv (cv x9) (cfv (cv x4) c1st)) (cfv (cv x2) cco))))))))))) ⟶ wceq cinito (cmpt (λ x1 . ccat) (λ x1 . crab (λ x2 . wral (λ x3 . weu (λ x4 . wcel (cv x4) (co (cv x2) (cv x3) (cfv (cv x1) chom)))) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq ctermo (cmpt (λ x1 . ccat) (λ x1 . crab (λ x2 . wral (λ x3 . weu (λ x4 . wcel (cv x4) (co (cv x3) (cv x2) (cfv (cv x1) chom)))) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq czeroo (cmpt (λ x1 . ccat) (λ x1 . cin (cfv (cv x1) cinito) (cfv (cv x1) ctermo))) ⟶ wceq cdoma (ccom c1st c1st) ⟶ x0) ⟶ x0
Axiom df_coda__df_homa__df_arw__df_ida__df_coa__df_setc__df_catc__df_estrc__df_xpc__df_1stf__df_2ndf__df_prf__df_evlf__df_curf__df_uncf__df_diag__df_hof__df_yon : ∀ x0 : ο . (wceq ccoda (ccom c2nd c1st) ⟶ wceq choma (cmpt (λ x1 . ccat) (λ x1 . cmpt (λ x2 . cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs)) (λ x2 . cxp (csn (cv x2)) (cfv (cv x2) (cfv (cv x1) chom))))) ⟶ wceq carw (cmpt (λ x1 . ccat) (λ x1 . cuni (crn (cfv (cv x1) choma)))) ⟶ wceq cida (cmpt (λ x1 . ccat) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . cotp (cv x2) (cv x2) (cfv (cv x2) (cfv (cv x1) ccid))))) ⟶ wceq ccoa (cmpt (λ x1 . ccat) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) carw) (λ x2 x3 . crab (λ x4 . wceq (cfv (cv x4) ccoda) (cfv (cv x2) cdoma)) (λ x4 . cfv (cv x1) carw)) (λ x2 x3 . cotp (cfv (cv x3) cdoma) (cfv (cv x2) ccoda) (co (cfv (cv x2) c2nd) (cfv (cv x3) c2nd) (co (cop (cfv (cv x3) cdoma) (cfv (cv x2) cdoma)) (cfv (cv x2) ccoda) (cfv (cv x1) cco)))))) ⟶ wceq csetc (cmpt (λ x1 . cvv) (λ x1 . ctp (cop (cfv cnx cbs) (cv x1)) (cop (cfv cnx chom) (cmpt2 (λ x2 x3 . cv x1) (λ x2 x3 . cv x1) (λ x2 x3 . co (cv x3) (cv x2) cmap))) (cop (cfv cnx cco) (cmpt2 (λ x2 x3 . cxp (cv x1) (cv x1)) (λ x2 x3 . cv x1) (λ x2 x3 . cmpt2 (λ x4 x5 . co (cv x3) (cfv (cv x2) c2nd) cmap) (λ x4 x5 . co (cfv (cv x2) c2nd) (cfv (cv x2) c1st) cmap) (λ x4 x5 . ccom (cv x4) (cv x5))))))) ⟶ wceq ccatc (cmpt (λ x1 . cvv) (λ x1 . csb (cin (cv x1) ccat) (λ x2 . ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx chom) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . co (cv x3) (cv x4) cfunc))) (cop (cfv cnx cco) (cmpt2 (λ x3 x4 . cxp (cv x2) (cv x2)) (λ x3 x4 . cv x2) (λ x3 x4 . cmpt2 (λ x5 x6 . co (cfv (cv x3) c2nd) (cv x4) cfunc) (λ x5 x6 . cfv (cv x3) cfunc) (λ x5 x6 . co (cv x5) (cv x6) ccofu))))))) ⟶ wceq cestrc (cmpt (λ x1 . cvv) (λ x1 . ctp (cop (cfv cnx cbs) (cv x1)) (cop (cfv cnx chom) (cmpt2 (λ x2 x3 . cv x1) (λ x2 x3 . cv x1) (λ x2 x3 . co (cfv (cv x3) cbs) (cfv (cv x2) cbs) cmap))) (cop (cfv cnx cco) (cmpt2 (λ x2 x3 . cxp (cv x1) (cv x1)) (λ x2 x3 . cv x1) (λ x2 x3 . cmpt2 (λ x4 x5 . co (cfv (cv x3) cbs) (cfv (cfv (cv x2) c2nd) cbs) cmap) (λ x4 x5 . co (cfv (cfv (cv x2) c2nd) cbs) (cfv (cfv (cv x2) c1st) cbs) cmap) (λ x4 x5 . ccom (cv x4) (cv x5))))))) ⟶ wceq cxpc (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cxp (cfv (cv x1) cbs) (cfv (cv x2) cbs)) (λ x3 . csb (cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . cxp (co (cfv (cv x4) c1st) (cfv (cv x5) c1st) (cfv (cv x1) chom)) (co (cfv (cv x4) c2nd) (cfv (cv x5) c2nd) (cfv (cv x2) chom)))) (λ x4 . ctp (cop (cfv cnx cbs) (cv x3)) (cop (cfv cnx chom) (cv x4)) (cop (cfv cnx cco) (cmpt2 (λ x5 x6 . cxp (cv x3) (cv x3)) (λ x5 x6 . cv x3) (λ x5 x6 . cmpt2 (λ x7 x8 . co (cfv (cv x5) c2nd) (cv x6) (cv x4)) (λ x7 x8 . cfv (cv x5) (cv x4)) (λ x7 x8 . cop (co (cfv (cv x7) c1st) (cfv (cv x8) c1st) (co (cop (cfv (cfv (cv x5) c1st) c1st) (cfv (cfv (cv x5) c2nd) c1st)) (cfv (cv x6) c1st) (cfv (cv x1) cco))) (co (cfv (cv x7) c2nd) (cfv (cv x8) c2nd) (co (cop (cfv (cfv (cv x5) c1st) c2nd) (cfv (cfv (cv x5) c2nd) c2nd)) (cfv (cv x6) c2nd) (cfv (cv x2) cco))))))))))) ⟶ wceq c1stf (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . csb (cxp (cfv (cv x1) cbs) (cfv (cv x2) cbs)) (λ x3 . cop (cres c1st (cv x3)) (cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . cres c1st (co (cv x4) (cv x5) (cfv (co (cv x1) (cv x2) cxpc) chom))))))) ⟶ wceq c2ndf (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . csb (cxp (cfv (cv x1) cbs) (cfv (cv x2) cbs)) (λ x3 . cop (cres c2nd (cv x3)) (cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . cres c2nd (co (cv x4) (cv x5) (cfv (co (cv x1) (cv x2) cxpc) chom))))))) ⟶ wceq cprf (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cdm (cfv (cv x1) c1st)) (λ x3 . cop (cmpt (λ x4 . cv x3) (λ x4 . cop (cfv (cv x4) (cfv (cv x1) c1st)) (cfv (cv x4) (cfv (cv x2) c1st)))) (cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . cmpt (λ x6 . cdm (co (cv x4) (cv x5) (cfv (cv x1) c2nd))) (λ x6 . cop (cfv (cv x6) (co (cv x4) (cv x5) (cfv (cv x1) c2nd))) (cfv (cv x6) (co (cv x4) (cv x5) (cfv (cv x2) c2nd))))))))) ⟶ wceq cevlf (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . cop (cmpt2 (λ x3 x4 . co (cv x1) (cv x2) cfunc) (λ x3 x4 . cfv (cv x1) cbs) (λ x3 x4 . cfv (cv x4) (cfv (cv x3) c1st))) (cmpt2 (λ x3 x4 . cxp (co (cv x1) (cv x2) cfunc) (cfv (cv x1) cbs)) (λ x3 x4 . cxp (co (cv x1) (cv x2) cfunc) (cfv (cv x1) cbs)) (λ x3 x4 . csb (cfv (cv x3) c1st) (λ x5 . csb (cfv (cv x4) c1st) (λ x6 . cmpt2 (λ x7 x8 . co (cv x5) (cv x6) (co (cv x1) (cv x2) cnat)) (λ x7 x8 . co (cfv (cv x3) c2nd) (cfv (cv x4) c2nd) (cfv (cv x1) chom)) (λ x7 x8 . co (cfv (cfv (cv x4) c2nd) (cv x7)) (cfv (cv x8) (co (cfv (cv x3) c2nd) (cfv (cv x4) c2nd) (cfv (cv x5) c2nd))) (co (cop (cfv (cfv (cv x3) c2nd) (cfv (cv x5) c1st)) (cfv (cfv (cv x4) c2nd) (cfv (cv x5) c1st))) (cfv (cfv (cv x4) c2nd) (cfv (cv x6) c1st)) (cfv (cv x2) cco))))))))) ⟶ wceq ccurf (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x1) c1st) (λ x3 . csb (cfv (cv x1) c2nd) (λ x4 . cop (cmpt (λ x5 . cfv (cv x3) cbs) (λ x5 . cop (cmpt (λ x6 . cfv (cv x4) cbs) (λ x6 . co (cv x5) (cv x6) (cfv (cv x2) c1st))) (cmpt2 (λ x6 x7 . cfv (cv x4) cbs) (λ x6 x7 . cfv (cv x4) cbs) (λ x6 x7 . cmpt (λ x8 . co (cv x6) (cv x7) (cfv (cv x4) chom)) (λ x8 . co (cfv (cv x5) (cfv (cv x3) ccid)) (cv x8) (co (cop (cv x5) (cv x6)) (cop (cv x5) (cv x7)) (cfv (cv x2) c2nd))))))) (cmpt2 (λ x5 x6 . cfv (cv x3) cbs) (λ x5 x6 . cfv (cv x3) cbs) (λ x5 x6 . cmpt (λ x7 . co (cv x5) (cv x6) (cfv (cv x3) chom)) (λ x7 . cmpt (λ x8 . cfv (cv x4) cbs) (λ x8 . co (cv x7) (cfv (cv x8) (cfv (cv x4) ccid)) (co (cop (cv x5) (cv x8)) (cop (cv x6) (cv x8)) (cfv (cv x2) c2nd)))))))))) ⟶ wceq cuncf (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cfv c1 (cv x1)) (cfv c2 (cv x1)) cevlf) (co (co (cv x2) (co (cfv cc0 (cv x1)) (cfv c1 (cv x1)) c1stf) ccofu) (co (cfv cc0 (cv x1)) (cfv c1 (cv x1)) c2ndf) cprf) ccofu)) ⟶ wceq cdiag (cmpt2 (λ x1 x2 . ccat) (λ x1 x2 . ccat) (λ x1 x2 . co (cop (cv x1) (cv x2)) (co (cv x1) (cv x2) c1stf) ccurf)) ⟶ wceq chof (cmpt (λ x1 . ccat) (λ x1 . cop (cfv (cv x1) chomf) (csb (cfv (cv x1) cbs) (λ x2 . cmpt2 (λ x3 x4 . cxp (cv x2) (cv x2)) (λ x3 x4 . cxp (cv x2) (cv x2)) (λ x3 x4 . cmpt2 (λ x5 x6 . co (cfv (cv x4) c1st) (cfv (cv x3) c1st) (cfv (cv x1) chom)) (λ x5 x6 . co (cfv (cv x3) c2nd) (cfv (cv x4) c2nd) (cfv (cv x1) chom)) (λ x5 x6 . cmpt (λ x7 . cfv (cv x3) (cfv (cv x1) chom)) (λ x7 . co (co (cv x6) (cv x7) (co (cv x3) (cfv (cv x4) c2nd) (cfv (cv x1) cco))) (cv x5) (co (cop (cfv (cv x4) c1st) (cfv (cv x3) c1st)) (cfv (cv x4) c2nd) (cfv (cv x1) cco))))))))) ⟶ wceq cyon (cmpt (λ x1 . ccat) (λ x1 . co (cop (cv x1) (cfv (cv x1) coppc)) (cfv (cfv (cv x1) coppc) chof) ccurf)) ⟶ x0) ⟶ x0
Axiom df_preset__df_drs__df_poset__df_plt__df_lub__df_glb__df_join__df_meet__df_toset__df_p0__df_p1__df_lat__df_clat__df_odu__df_ipo__df_dlat__df_ps__df_tsr : ∀ x0 : ο . (wceq cpreset (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wa (wbr (cv x4) (cv x4) (cv x3)) (wa (wbr (cv x4) (cv x5) (cv x3)) (wbr (cv x5) (cv x6) (cv x3)) ⟶ wbr (cv x4) (cv x6) (cv x3))) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) cple)) (cfv (cv x1) cbs))) ⟶ wceq cdrs (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wa (wne (cv x2) c0) (wral (λ x4 . wral (λ x5 . wrex (λ x6 . wa (wbr (cv x4) (cv x6) (cv x3)) (wbr (cv x5) (cv x6) (cv x3))) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2))) (cfv (cv x1) cple)) (cfv (cv x1) cbs)) (λ x1 . cpreset)) ⟶ wceq cpo (cab (λ x1 . wex (λ x2 . wex (λ x3 . w3a (wceq (cv x2) (cfv (cv x1) cbs)) (wceq (cv x3) (cfv (cv x1) cple)) (wral (λ x4 . wral (λ x5 . wral (λ x6 . w3a (wbr (cv x4) (cv x4) (cv x3)) (wa (wbr (cv x4) (cv x5) (cv x3)) (wbr (cv x5) (cv x4) (cv x3)) ⟶ wceq (cv x4) (cv x5)) (wa (wbr (cv x4) (cv x5) (cv x3)) (wbr (cv x5) (cv x6) (cv x3)) ⟶ wbr (cv x4) (cv x6) (cv x3))) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)))))) ⟶ wceq cplt (cmpt (λ x1 . cvv) (λ x1 . cdif (cfv (cv x1) cple) cid)) ⟶ wceq club (cmpt (λ x1 . cvv) (λ x1 . cres (cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . crio (λ x3 . wa (wral (λ x4 . wbr (cv x4) (cv x3) (cfv (cv x1) cple)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wbr (cv x5) (cv x4) (cfv (cv x1) cple)) (λ x5 . cv x2) ⟶ wbr (cv x3) (cv x4) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs))) (λ x3 . cfv (cv x1) cbs))) (cab (λ x2 . wreu (λ x3 . wa (wral (λ x4 . wbr (cv x4) (cv x3) (cfv (cv x1) cple)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wbr (cv x5) (cv x4) (cfv (cv x1) cple)) (λ x5 . cv x2) ⟶ wbr (cv x3) (cv x4) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs))) (λ x3 . cfv (cv x1) cbs))))) ⟶ wceq cglb (cmpt (λ x1 . cvv) (λ x1 . cres (cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . crio (λ x3 . wa (wral (λ x4 . wbr (cv x3) (cv x4) (cfv (cv x1) cple)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wbr (cv x4) (cv x5) (cfv (cv x1) cple)) (λ x5 . cv x2) ⟶ wbr (cv x4) (cv x3) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs))) (λ x3 . cfv (cv x1) cbs))) (cab (λ x2 . wreu (λ x3 . wa (wral (λ x4 . wbr (cv x3) (cv x4) (cfv (cv x1) cple)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wbr (cv x4) (cv x5) (cfv (cv x1) cple)) (λ x5 . cv x2) ⟶ wbr (cv x4) (cv x3) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs))) (λ x3 . cfv (cv x1) cbs))))) ⟶ wceq cjn (cmpt (λ x1 . cvv) (λ x1 . coprab (λ x2 x3 x4 . wbr (cpr (cv x2) (cv x3)) (cv x4) (cfv (cv x1) club)))) ⟶ wceq cmee (cmpt (λ x1 . cvv) (λ x1 . coprab (λ x2 x3 x4 . wbr (cpr (cv x2) (cv x3)) (cv x4) (cfv (cv x1) cglb)))) ⟶ wceq ctos (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wo (wbr (cv x4) (cv x5) (cv x3)) (wbr (cv x5) (cv x4) (cv x3))) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) cple)) (cfv (cv x1) cbs)) (λ x1 . cpo)) ⟶ wceq cp0 (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cbs) (cfv (cv x1) cglb))) ⟶ wceq cp1 (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cbs) (cfv (cv x1) club))) ⟶ wceq clat (crab (λ x1 . wa (wceq (cdm (cfv (cv x1) cjn)) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs))) (wceq (cdm (cfv (cv x1) cmee)) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs)))) (λ x1 . cpo)) ⟶ wceq ccla (crab (λ x1 . wa (wceq (cdm (cfv (cv x1) club)) (cpw (cfv (cv x1) cbs))) (wceq (cdm (cfv (cv x1) cglb)) (cpw (cfv (cv x1) cbs)))) (λ x1 . cpo)) ⟶ wceq codu (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cop (cfv cnx cple) (ccnv (cfv (cv x1) cple))) csts)) ⟶ wceq cipo (cmpt (λ x1 . cvv) (λ x1 . csb (copab (λ x2 x3 . wa (wss (cpr (cv x2) (cv x3)) (cv x1)) (wss (cv x2) (cv x3)))) (λ x2 . cun (cpr (cop (cfv cnx cbs) (cv x1)) (cop (cfv cnx cts) (cfv (cv x2) cordt))) (cpr (cop (cfv cnx cple) (cv x2)) (cop (cfv cnx coc) (cmpt (λ x3 . cv x1) (λ x3 . cuni (crab (λ x4 . wceq (cin (cv x4) (cv x3)) c0) (λ x4 . cv x1))))))))) ⟶ wceq cdlat (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wceq (co (cv x5) (co (cv x6) (cv x7) (cv x3)) (cv x4)) (co (co (cv x5) (cv x6) (cv x4)) (co (cv x5) (cv x7) (cv x4)) (cv x3))) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (cfv (cv x1) cmee)) (cfv (cv x1) cjn)) (cfv (cv x1) cbs)) (λ x1 . clat)) ⟶ wceq cps (cab (λ x1 . w3a (wrel (cv x1)) (wss (ccom (cv x1) (cv x1)) (cv x1)) (wceq (cin (cv x1) (ccnv (cv x1))) (cres cid (cuni (cuni (cv x1))))))) ⟶ wceq ctsr (crab (λ x1 . wss (cxp (cdm (cv x1)) (cdm (cv x1))) (cun (cv x1) (ccnv (cv x1)))) (λ x1 . cps)) ⟶ x0) ⟶ x0
Axiom df_dir__df_tail__df_plusf__df_mgm__df_sgrp__df_mnd__df_mhm__df_submnd__df_frmd__df_vrmd__df_grp__df_minusg__df_sbg__df_mulg__df_subg__df_nsg__df_eqg__df_ghm : ∀ x0 : ο . (wceq cdir (cab (λ x1 . wa (wa (wrel (cv x1)) (wss (cres cid (cuni (cuni (cv x1)))) (cv x1))) (wa (wss (ccom (cv x1) (cv x1)) (cv x1)) (wss (cxp (cuni (cuni (cv x1))) (cuni (cuni (cv x1)))) (ccom (ccnv (cv x1)) (cv x1)))))) ⟶ wceq ctail (cmpt (λ x1 . cdir) (λ x1 . cmpt (λ x2 . cuni (cuni (cv x1))) (λ x2 . cima (cv x1) (csn (cv x2))))) ⟶ wceq cplusf (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . co (cv x2) (cv x3) (cfv (cv x1) cplusg)))) ⟶ wceq cmgm (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wcel (co (cv x4) (cv x5) (cv x3)) (cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs))) ⟶ wceq csgrp (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wceq (co (co (cv x4) (cv x5) (cv x3)) (cv x6) (cv x3)) (co (cv x4) (co (cv x5) (cv x6) (cv x3)) (cv x3))) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x1 . cmgm)) ⟶ wceq cmnd (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wrex (λ x4 . wral (λ x5 . wa (wceq (co (cv x4) (cv x5) (cv x3)) (cv x5)) (wceq (co (cv x5) (cv x4) (cv x3)) (cv x5))) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x1 . csgrp)) ⟶ wceq cmhm (cmpt2 (λ x1 x2 . cmnd) (λ x1 x2 . cmnd) (λ x1 x2 . crab (λ x3 . wa (wral (λ x4 . wral (λ x5 . wceq (cfv (co (cv x4) (cv x5) (cfv (cv x1) cplusg)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) cplusg))) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs)) (wceq (cfv (cfv (cv x1) c0g) (cv x3)) (cfv (cv x2) c0g))) (λ x3 . co (cfv (cv x2) cbs) (cfv (cv x1) cbs) cmap))) ⟶ wceq csubmnd (cmpt (λ x1 . cmnd) (λ x1 . crab (λ x2 . wa (wcel (cfv (cv x1) c0g) (cv x2)) (wral (λ x3 . wral (λ x4 . wcel (co (cv x3) (cv x4) (cfv (cv x1) cplusg)) (cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2))) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq cfrmd (cmpt (λ x1 . cvv) (λ x1 . cpr (cop (cfv cnx cbs) (cword (cv x1))) (cop (cfv cnx cplusg) (cres cconcat (cxp (cword (cv x1)) (cword (cv x1))))))) ⟶ wceq cvrmd (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cv x1) (λ x2 . cs1 (cv x2)))) ⟶ wceq cgrp (crab (λ x1 . wral (λ x2 . wrex (λ x3 . wceq (co (cv x3) (cv x2) (cfv (cv x1) cplusg)) (cfv (cv x1) c0g)) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs)) (λ x1 . cmnd)) ⟶ wceq cminusg (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . crio (λ x3 . wceq (co (cv x3) (cv x2) (cfv (cv x1) cplusg)) (cfv (cv x1) c0g)) (λ x3 . cfv (cv x1) cbs)))) ⟶ wceq csg (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . co (cv x2) (cfv (cv x3) (cfv (cv x1) cminusg)) (cfv (cv x1) cplusg)))) ⟶ wceq cmg (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cz) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cif (wceq (cv x2) cc0) (cfv (cv x1) c0g) (csb (cseq (cfv (cv x1) cplusg) (cxp cn (csn (cv x3))) c1) (λ x4 . cif (wbr cc0 (cv x2) clt) (cfv (cv x2) (cv x4)) (cfv (cfv (cneg (cv x2)) (cv x4)) (cfv (cv x1) cminusg))))))) ⟶ wceq csubg (cmpt (λ x1 . cgrp) (λ x1 . crab (λ x2 . wcel (co (cv x1) (cv x2) cress) cgrp) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq cnsg (cmpt (λ x1 . cgrp) (λ x1 . crab (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wral (λ x5 . wral (λ x6 . wb (wcel (co (cv x5) (cv x6) (cv x4)) (cv x2)) (wcel (co (cv x6) (cv x5) (cv x4)) (cv x2))) (λ x6 . cv x3)) (λ x5 . cv x3)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) csubg))) ⟶ wceq cqg (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . copab (λ x3 x4 . wa (wss (cpr (cv x3) (cv x4)) (cfv (cv x1) cbs)) (wcel (co (cfv (cv x3) (cfv (cv x1) cminusg)) (cv x4) (cfv (cv x1) cplusg)) (cv x2))))) ⟶ wceq cghm (cmpt2 (λ x1 x2 . cgrp) (λ x1 x2 . cgrp) (λ x1 x2 . cab (λ x3 . wsbc (λ x4 . wa (wf (cv x4) (cfv (cv x2) cbs) (cv x3)) (wral (λ x5 . wral (λ x6 . wceq (cfv (co (cv x5) (cv x6) (cfv (cv x1) cplusg)) (cv x3)) (co (cfv (cv x5) (cv x3)) (cfv (cv x6) (cv x3)) (cfv (cv x2) cplusg))) (λ x6 . cv x4)) (λ x5 . cv x4))) (cfv (cv x1) cbs)))) ⟶ x0) ⟶ x0
Axiom df_gim__df_gic__df_ga__df_cntz__df_cntr__df_oppg__df_symg__df_pmtr__df_psgn__df_evpm__df_od__df_gex__df_pgp__df_slw__df_lsm__df_pj1__df_efg__df_frgp : ∀ x0 : ο . (wceq cgim (cmpt2 (λ x1 x2 . cgrp) (λ x1 x2 . cgrp) (λ x1 x2 . crab (λ x3 . wf1o (cfv (cv x1) cbs) (cfv (cv x2) cbs) (cv x3)) (λ x3 . co (cv x1) (cv x2) cghm))) ⟶ wceq cgic (cima (ccnv cgim) (cdif cvv c1o)) ⟶ wceq cga (cmpt2 (λ x1 x2 . cgrp) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x1) cbs) (λ x3 . crab (λ x4 . wral (λ x5 . wa (wceq (co (cfv (cv x1) c0g) (cv x5) (cv x4)) (cv x5)) (wral (λ x6 . wral (λ x7 . wceq (co (co (cv x6) (cv x7) (cfv (cv x1) cplusg)) (cv x5) (cv x4)) (co (cv x6) (co (cv x7) (cv x5) (cv x4)) (cv x4))) (λ x7 . cv x3)) (λ x6 . cv x3))) (λ x5 . cv x2)) (λ x4 . co (cv x2) (cxp (cv x3) (cv x2)) cmap)))) ⟶ wceq ccntz (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . crab (λ x3 . wral (λ x4 . wceq (co (cv x3) (cv x4) (cfv (cv x1) cplusg)) (co (cv x4) (cv x3) (cfv (cv x1) cplusg))) (λ x4 . cv x2)) (λ x3 . cfv (cv x1) cbs)))) ⟶ wceq ccntr (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cbs) (cfv (cv x1) ccntz))) ⟶ wceq coppg (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cop (cfv cnx cplusg) (ctpos (cfv (cv x1) cplusg))) csts)) ⟶ wceq csymg (cmpt (λ x1 . cvv) (λ x1 . csb (cab (λ x2 . wf1o (cv x1) (cv x1) (cv x2))) (λ x2 . ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . ccom (cv x3) (cv x4)))) (cop (cfv cnx cts) (cfv (cxp (cv x1) (csn (cpw (cv x1)))) cpt))))) ⟶ wceq cpmtr (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . crab (λ x3 . wbr (cv x3) c2o cen) (λ x3 . cpw (cv x1))) (λ x2 . cmpt (λ x3 . cv x1) (λ x3 . cif (wcel (cv x3) (cv x2)) (cuni (cdif (cv x2) (csn (cv x3)))) (cv x3))))) ⟶ wceq cpsgn (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . crab (λ x3 . wcel (cdm (cdif (cv x3) cid)) cfn) (λ x3 . cfv (cfv (cv x1) csymg) cbs)) (λ x2 . cio (λ x3 . wrex (λ x4 . wa (wceq (cv x2) (co (cfv (cv x1) csymg) (cv x4) cgsu)) (wceq (cv x3) (co (cneg c1) (cfv (cv x4) chash) cexp))) (λ x4 . cword (crn (cfv (cv x1) cpmtr))))))) ⟶ wceq cevpm (cmpt (λ x1 . cvv) (λ x1 . cima (ccnv (cfv (cv x1) cpsgn)) (csn c1))) ⟶ wceq cod (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . csb (crab (λ x3 . wceq (co (cv x3) (cv x2) (cfv (cv x1) cmg)) (cfv (cv x1) c0g)) (λ x3 . cn)) (λ x3 . cif (wceq (cv x3) c0) cc0 (cinf (cv x3) cr clt))))) ⟶ wceq cgex (cmpt (λ x1 . cvv) (λ x1 . csb (crab (λ x2 . wral (λ x3 . wceq (co (cv x2) (cv x3) (cfv (cv x1) cmg)) (cfv (cv x1) c0g)) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cn)) (λ x2 . cif (wceq (cv x2) c0) cc0 (cinf (cv x2) cr clt)))) ⟶ wceq cpgp (copab (λ x1 x2 . wa (wa (wcel (cv x1) cprime) (wcel (cv x2) cgrp)) (wral (λ x3 . wrex (λ x4 . wceq (cfv (cv x3) (cfv (cv x2) cod)) (co (cv x1) (cv x4) cexp)) (λ x4 . cn0)) (λ x3 . cfv (cv x2) cbs)))) ⟶ wceq cslw (cmpt2 (λ x1 x2 . cprime) (λ x1 x2 . cgrp) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wb (wa (wss (cv x3) (cv x4)) (wbr (cv x1) (co (cv x2) (cv x4) cress) cpgp)) (wceq (cv x3) (cv x4))) (λ x4 . cfv (cv x2) csubg)) (λ x3 . cfv (cv x2) csubg))) ⟶ wceq clsm (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cpw (cfv (cv x1) cbs)) (λ x2 x3 . cpw (cfv (cv x1) cbs)) (λ x2 x3 . crn (cmpt2 (λ x4 x5 . cv x2) (λ x4 x5 . cv x3) (λ x4 x5 . co (cv x4) (cv x5) (cfv (cv x1) cplusg)))))) ⟶ wceq cpj1 (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cpw (cfv (cv x1) cbs)) (λ x2 x3 . cpw (cfv (cv x1) cbs)) (λ x2 x3 . cmpt (λ x4 . co (cv x2) (cv x3) (cfv (cv x1) clsm)) (λ x4 . crio (λ x5 . wrex (λ x6 . wceq (cv x4) (co (cv x5) (cv x6) (cfv (cv x1) cplusg))) (λ x6 . cv x3)) (λ x5 . cv x2))))) ⟶ wceq cefg (cmpt (λ x1 . cvv) (λ x1 . cint (cab (λ x2 . wa (wer (cword (cxp (cv x1) c2o)) (cv x2)) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wbr (cv x3) (co (cv x3) (cotp (cv x4) (cv x4) (cs2 (cop (cv x5) (cv x6)) (cop (cv x5) (cdif c1o (cv x6))))) csplice) (cv x2)) (λ x6 . c2o)) (λ x5 . cv x1)) (λ x4 . co cc0 (cfv (cv x3) chash) cfz)) (λ x3 . cword (cxp (cv x1) c2o))))))) ⟶ wceq cfrgp (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cxp (cv x1) c2o) cfrmd) (cfv (cv x1) cefg) cqus)) ⟶ x0) ⟶ x0
Axiom df_vrgp__df_cmn__df_abl__df_cyg__df_dprd__df_dpj__df_mgp__df_ur__df_srg__df_ring__df_cring__df_oppr__df_dvdsr__df_unit__df_irred__df_invr__df_dvr__df_rprm : ∀ x0 : ο . (wceq cvrgp (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cv x1) (λ x2 . cec (cs1 (cop (cv x2) c0)) (cfv (cv x1) cefg)))) ⟶ wceq ccmn (crab (λ x1 . wral (λ x2 . wral (λ x3 . wceq (co (cv x2) (cv x3) (cfv (cv x1) cplusg)) (co (cv x3) (cv x2) (cfv (cv x1) cplusg))) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs)) (λ x1 . cmnd)) ⟶ wceq cabl (cin cgrp ccmn) ⟶ wceq ccyg (crab (λ x1 . wrex (λ x2 . wceq (crn (cmpt (λ x3 . cz) (λ x3 . co (cv x3) (cv x2) (cfv (cv x1) cmg)))) (cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs)) (λ x1 . cgrp)) ⟶ wceq cdprd (cmpt2 (λ x1 x2 . cgrp) (λ x1 x2 . cab (λ x3 . wa (wf (cdm (cv x3)) (cfv (cv x1) csubg) (cv x3)) (wral (λ x4 . wa (wral (λ x5 . wss (cfv (cv x4) (cv x3)) (cfv (cfv (cv x5) (cv x3)) (cfv (cv x1) ccntz))) (λ x5 . cdif (cdm (cv x3)) (csn (cv x4)))) (wceq (cin (cfv (cv x4) (cv x3)) (cfv (cuni (cima (cv x3) (cdif (cdm (cv x3)) (csn (cv x4))))) (cfv (cfv (cv x1) csubg) cmrc))) (csn (cfv (cv x1) c0g)))) (λ x4 . cdm (cv x3))))) (λ x1 x2 . crn (cmpt (λ x3 . crab (λ x4 . wbr (cv x4) (cfv (cv x1) c0g) cfsupp) (λ x4 . cixp (λ x5 . cdm (cv x2)) (λ x5 . cfv (cv x5) (cv x2)))) (λ x3 . co (cv x1) (cv x3) cgsu)))) ⟶ wceq cdpj (cmpt2 (λ x1 x2 . cgrp) (λ x1 x2 . cima (cdm cdprd) (csn (cv x1))) (λ x1 x2 . cmpt (λ x3 . cdm (cv x2)) (λ x3 . co (cfv (cv x3) (cv x2)) (co (cv x1) (cres (cv x2) (cdif (cdm (cv x2)) (csn (cv x3)))) cdprd) (cfv (cv x1) cpj1)))) ⟶ wceq cmgp (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cop (cfv cnx cplusg) (cfv (cv x1) cmulr)) csts)) ⟶ wceq cur (ccom c0g cmgp) ⟶ wceq csrg (crab (λ x1 . wa (wcel (cfv (cv x1) cmgp) cmnd) (wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wral (λ x6 . wa (wral (λ x7 . wral (λ x8 . wa (wceq (co (cv x6) (co (cv x7) (cv x8) (cv x3)) (cv x4)) (co (co (cv x6) (cv x7) (cv x4)) (co (cv x6) (cv x8) (cv x4)) (cv x3))) (wceq (co (co (cv x6) (cv x7) (cv x3)) (cv x8) (cv x4)) (co (co (cv x6) (cv x8) (cv x4)) (co (cv x7) (cv x8) (cv x4)) (cv x3)))) (λ x8 . cv x2)) (λ x7 . cv x2)) (wa (wceq (co (cv x5) (cv x6) (cv x4)) (cv x5)) (wceq (co (cv x6) (cv x5) (cv x4)) (cv x5)))) (λ x6 . cv x2)) (cfv (cv x1) c0g)) (cfv (cv x1) cmulr)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs))) (λ x1 . ccmn)) ⟶ wceq crg (crab (λ x1 . wa (wcel (cfv (cv x1) cmgp) cmnd) (wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wa (wceq (co (cv x5) (co (cv x6) (cv x7) (cv x3)) (cv x4)) (co (co (cv x5) (cv x6) (cv x4)) (co (cv x5) (cv x7) (cv x4)) (cv x3))) (wceq (co (co (cv x5) (cv x6) (cv x3)) (cv x7) (cv x4)) (co (co (cv x5) (cv x7) (cv x4)) (co (cv x6) (cv x7) (cv x4)) (cv x3)))) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (cfv (cv x1) cmulr)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs))) (λ x1 . cgrp)) ⟶ wceq ccrg (crab (λ x1 . wcel (cfv (cv x1) cmgp) ccmn) (λ x1 . crg)) ⟶ wceq coppr (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cop (cfv cnx cmulr) (ctpos (cfv (cv x1) cmulr))) csts)) ⟶ wceq cdsr (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wcel (cv x2) (cfv (cv x1) cbs)) (wrex (λ x4 . wceq (co (cv x4) (cv x2) (cfv (cv x1) cmulr)) (cv x3)) (λ x4 . cfv (cv x1) cbs))))) ⟶ wceq cui (cmpt (λ x1 . cvv) (λ x1 . cima (ccnv (cin (cfv (cv x1) cdsr) (cfv (cfv (cv x1) coppr) cdsr))) (csn (cfv (cv x1) cur)))) ⟶ wceq cir (cmpt (λ x1 . cvv) (λ x1 . csb (cdif (cfv (cv x1) cbs) (cfv (cv x1) cui)) (λ x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wne (co (cv x4) (cv x5) (cfv (cv x1) cmulr)) (cv x3)) (λ x5 . cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2)))) ⟶ wceq cinvr (cmpt (λ x1 . cvv) (λ x1 . cfv (co (cfv (cv x1) cmgp) (cfv (cv x1) cui) cress) cminusg)) ⟶ wceq cdvr (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cui) (λ x2 x3 . co (cv x2) (cfv (cv x3) (cfv (cv x1) cinvr)) (cfv (cv x1) cmulr)))) ⟶ wceq crpm (cmpt (λ x1 . cvv) (λ x1 . csb (cfv (cv x1) cbs) (λ x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wsbc (λ x6 . wbr (cv x3) (co (cv x4) (cv x5) (cfv (cv x1) cmulr)) (cv x6) ⟶ wo (wbr (cv x3) (cv x4) (cv x6)) (wbr (cv x3) (cv x5) (cv x6))) (cfv (cv x1) cdsr)) (λ x5 . cv x2)) (λ x4 . cv x2)) (λ x3 . cdif (cv x2) (cun (cfv (cv x1) cui) (csn (cfv (cv x1) c0g))))))) ⟶ x0) ⟶ x0
Axiom df_rnghom__df_rngiso__df_ric__df_drng__df_field__df_subrg__df_rgspn__df_abv__df_staf__df_srng__df_lmod__df_scaf__df_lss__df_lsp__df_lmhm__df_lmim__df_lmic__df_lbs : ∀ x0 : ο . (wceq crh (cmpt2 (λ x1 x2 . crg) (λ x1 x2 . crg) (λ x1 x2 . csb (cfv (cv x1) cbs) (λ x3 . csb (cfv (cv x2) cbs) (λ x4 . crab (λ x5 . wa (wceq (cfv (cfv (cv x1) cur) (cv x5)) (cfv (cv x2) cur)) (wral (λ x6 . wral (λ x7 . wa (wceq (cfv (co (cv x6) (cv x7) (cfv (cv x1) cplusg)) (cv x5)) (co (cfv (cv x6) (cv x5)) (cfv (cv x7) (cv x5)) (cfv (cv x2) cplusg))) (wceq (cfv (co (cv x6) (cv x7) (cfv (cv x1) cmulr)) (cv x5)) (co (cfv (cv x6) (cv x5)) (cfv (cv x7) (cv x5)) (cfv (cv x2) cmulr)))) (λ x7 . cv x3)) (λ x6 . cv x3))) (λ x5 . co (cv x4) (cv x3) cmap))))) ⟶ wceq crs (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wcel (ccnv (cv x3)) (co (cv x2) (cv x1) crh)) (λ x3 . co (cv x1) (cv x2) crh))) ⟶ wceq cric (cima (ccnv crs) (cdif cvv c1o)) ⟶ wceq cdr (crab (λ x1 . wceq (cfv (cv x1) cui) (cdif (cfv (cv x1) cbs) (csn (cfv (cv x1) c0g)))) (λ x1 . crg)) ⟶ wceq cfield (cin cdr ccrg) ⟶ wceq csubrg (cmpt (λ x1 . crg) (λ x1 . crab (λ x2 . wa (wcel (co (cv x1) (cv x2) cress) crg) (wcel (cfv (cv x1) cur) (cv x2))) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq crgspn (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) csubrg))))) ⟶ wceq cabv (cmpt (λ x1 . crg) (λ x1 . crab (λ x2 . wral (λ x3 . wa (wb (wceq (cfv (cv x3) (cv x2)) cc0) (wceq (cv x3) (cfv (cv x1) c0g))) (wral (λ x4 . wa (wceq (cfv (co (cv x3) (cv x4) (cfv (cv x1) cmulr)) (cv x2)) (co (cfv (cv x3) (cv x2)) (cfv (cv x4) (cv x2)) cmul)) (wbr (cfv (co (cv x3) (cv x4) (cfv (cv x1) cplusg)) (cv x2)) (co (cfv (cv x3) (cv x2)) (cfv (cv x4) (cv x2)) caddc) cle)) (λ x4 . cfv (cv x1) cbs))) (λ x3 . cfv (cv x1) cbs)) (λ x2 . co (co cc0 cpnf cico) (cfv (cv x1) cbs) cmap))) ⟶ wceq cstf (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . cfv (cv x2) (cfv (cv x1) cstv)))) ⟶ wceq csr (cab (λ x1 . wsbc (λ x2 . wa (wcel (cv x2) (co (cv x1) (cfv (cv x1) coppr) crh)) (wceq (cv x2) (ccnv (cv x2)))) (cfv (cv x1) cstf))) ⟶ wceq clmod (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wsbc (λ x7 . wsbc (λ x8 . wa (wcel (cv x4) crg) (wral (λ x9 . wral (λ x10 . wral (λ x11 . wral (λ x12 . wa (w3a (wcel (co (cv x10) (cv x12) (cv x5)) (cv x2)) (wceq (co (cv x10) (co (cv x12) (cv x11) (cv x3)) (cv x5)) (co (co (cv x10) (cv x12) (cv x5)) (co (cv x10) (cv x11) (cv x5)) (cv x3))) (wceq (co (co (cv x9) (cv x10) (cv x7)) (cv x12) (cv x5)) (co (co (cv x9) (cv x12) (cv x5)) (co (cv x10) (cv x12) (cv x5)) (cv x3)))) (wa (wceq (co (co (cv x9) (cv x10) (cv x8)) (cv x12) (cv x5)) (co (cv x9) (co (cv x10) (cv x12) (cv x5)) (cv x5))) (wceq (co (cfv (cv x4) cur) (cv x12) (cv x5)) (cv x12)))) (λ x12 . cv x2)) (λ x11 . cv x2)) (λ x10 . cv x6)) (λ x9 . cv x6))) (cfv (cv x4) cmulr)) (cfv (cv x4) cplusg)) (cfv (cv x4) cbs)) (cfv (cv x1) cvsca)) (cfv (cv x1) csca)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x1 . cgrp)) ⟶ wceq cscaf (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cfv (cv x1) csca) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . co (cv x2) (cv x3) (cfv (cv x1) cvsca)))) ⟶ wceq clss (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wral (λ x4 . wral (λ x5 . wcel (co (co (cv x3) (cv x4) (cfv (cv x1) cvsca)) (cv x5) (cfv (cv x1) cplusg)) (cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (λ x3 . cfv (cfv (cv x1) csca) cbs)) (λ x2 . cdif (cpw (cfv (cv x1) cbs)) (csn c0)))) ⟶ wceq clspn (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) clss))))) ⟶ wceq clmhm (cmpt2 (λ x1 x2 . clmod) (λ x1 x2 . clmod) (λ x1 x2 . crab (λ x3 . wsbc (λ x4 . wa (wceq (cfv (cv x2) csca) (cv x4)) (wral (λ x5 . wral (λ x6 . wceq (cfv (co (cv x5) (cv x6) (cfv (cv x1) cvsca)) (cv x3)) (co (cv x5) (cfv (cv x6) (cv x3)) (cfv (cv x2) cvsca))) (λ x6 . cfv (cv x1) cbs)) (λ x5 . cfv (cv x4) cbs))) (cfv (cv x1) csca)) (λ x3 . co (cv x1) (cv x2) cghm))) ⟶ wceq clmim (cmpt2 (λ x1 x2 . clmod) (λ x1 x2 . clmod) (λ x1 x2 . crab (λ x3 . wf1o (cfv (cv x1) cbs) (cfv (cv x2) cbs) (cv x3)) (λ x3 . co (cv x1) (cv x2) clmhm))) ⟶ wceq clmic (cima (ccnv clmim) (cdif cvv c1o)) ⟶ wceq clbs (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wa (wceq (cfv (cv x2) (cv x3)) (cfv (cv x1) cbs)) (wral (λ x5 . wral (λ x6 . wn (wcel (co (cv x6) (cv x5) (cfv (cv x1) cvsca)) (cfv (cdif (cv x2) (csn (cv x5))) (cv x3)))) (λ x6 . cdif (cfv (cv x4) cbs) (csn (cfv (cv x4) c0g)))) (λ x5 . cv x2))) (cfv (cv x1) csca)) (cfv (cv x1) clspn)) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ x0) ⟶ x0
Axiom df_lvec__df_sra__df_rgmod__df_lidl__df_rsp__df_2idl__df_lpidl__df_lpir__df_nzr__df_rlreg__df_domn__df_idom__df_pid__df_assa__df_asp__df_ascl__df_psr__df_mvr : ∀ x0 : ο . (wceq clvec (crab (λ x1 . wcel (cfv (cv x1) csca) cdr) (λ x1 . clmod)) ⟶ wceq csra (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . co (co (co (cv x1) (cop (cfv cnx csca) (co (cv x1) (cv x2) cress)) csts) (cop (cfv cnx cvsca) (cfv (cv x1) cmulr)) csts) (cop (cfv cnx cip) (cfv (cv x1) cmulr)) csts))) ⟶ wceq crglmod (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cbs) (cfv (cv x1) csra))) ⟶ wceq clidl (ccom clss crglmod) ⟶ wceq crsp (ccom clspn crglmod) ⟶ wceq c2idl (cmpt (λ x1 . cvv) (λ x1 . cin (cfv (cv x1) clidl) (cfv (cfv (cv x1) coppr) clidl))) ⟶ wceq clpidl (cmpt (λ x1 . crg) (λ x1 . ciun (λ x2 . cfv (cv x1) cbs) (λ x2 . csn (cfv (csn (cv x2)) (cfv (cv x1) crsp))))) ⟶ wceq clpir (crab (λ x1 . wceq (cfv (cv x1) clidl) (cfv (cv x1) clpidl)) (λ x1 . crg)) ⟶ wceq cnzr (crab (λ x1 . wne (cfv (cv x1) cur) (cfv (cv x1) c0g)) (λ x1 . crg)) ⟶ wceq crlreg (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wceq (co (cv x2) (cv x3) (cfv (cv x1) cmulr)) (cfv (cv x1) c0g) ⟶ wceq (cv x3) (cfv (cv x1) c0g)) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq cdomn (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wceq (co (cv x4) (cv x5) (cfv (cv x1) cmulr)) (cv x3) ⟶ wo (wceq (cv x4) (cv x3)) (wceq (cv x5) (cv x3))) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) c0g)) (cfv (cv x1) cbs)) (λ x1 . cnzr)) ⟶ wceq cidom (cin ccrg cdomn) ⟶ wceq cpid (cin cidom clpir) ⟶ wceq casa (crab (λ x1 . wsbc (λ x2 . wa (wcel (cv x2) ccrg) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wsbc (λ x6 . wsbc (λ x7 . wa (wceq (co (co (cv x3) (cv x4) (cv x6)) (cv x5) (cv x7)) (co (cv x3) (co (cv x4) (cv x5) (cv x7)) (cv x6))) (wceq (co (cv x4) (co (cv x3) (cv x5) (cv x6)) (cv x7)) (co (cv x3) (co (cv x4) (cv x5) (cv x7)) (cv x6)))) (cfv (cv x1) cmulr)) (cfv (cv x1) cvsca)) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x2) cbs))) (cfv (cv x1) csca)) (λ x1 . cin clmod crg)) ⟶ wceq casp (cmpt (λ x1 . casa) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cin (cfv (cv x1) csubrg) (cfv (cv x1) clss)))))) ⟶ wceq cascl (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cfv (cv x1) csca) cbs) (λ x2 . co (cv x2) (cfv (cv x1) cur) (cfv (cv x1) cvsca)))) ⟶ wceq cmps (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (crab (λ x3 . wcel (cima (ccnv (cv x3)) cn) cfn) (λ x3 . co cn0 (cv x1) cmap)) (λ x3 . csb (co (cfv (cv x2) cbs) (cv x3) cmap) (λ x4 . cun (ctp (cop (cfv cnx cbs) (cv x4)) (cop (cfv cnx cplusg) (cres (cof (cfv (cv x2) cplusg)) (cxp (cv x4) (cv x4)))) (cop (cfv cnx cmulr) (cmpt2 (λ x5 x6 . cv x4) (λ x5 x6 . cv x4) (λ x5 x6 . cmpt (λ x7 . cv x3) (λ x7 . co (cv x2) (cmpt (λ x8 . crab (λ x9 . wbr (cv x9) (cv x7) (cofr cle)) (λ x9 . cv x3)) (λ x8 . co (cfv (cv x8) (cv x5)) (cfv (co (cv x7) (cv x8) (cof cmin)) (cv x6)) (cfv (cv x2) cmulr))) cgsu))))) (ctp (cop (cfv cnx csca) (cv x2)) (cop (cfv cnx cvsca) (cmpt2 (λ x5 x6 . cfv (cv x2) cbs) (λ x5 x6 . cv x4) (λ x5 x6 . co (cxp (cv x3) (csn (cv x5))) (cv x6) (cof (cfv (cv x2) cmulr))))) (cop (cfv cnx cts) (cfv (cxp (cv x3) (csn (cfv (cv x2) ctopn))) cpt))))))) ⟶ wceq cmvr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cv x1) (λ x3 . cmpt (λ x4 . crab (λ x5 . wcel (cima (ccnv (cv x5)) cn) cfn) (λ x5 . co cn0 (cv x1) cmap)) (λ x4 . cif (wceq (cv x4) (cmpt (λ x5 . cv x1) (λ x5 . cif (wceq (cv x5) (cv x3)) c1 cc0))) (cfv (cv x2) cur) (cfv (cv x2) c0g))))) ⟶ x0) ⟶ x0
Axiom df_mpl__df_ltbag__df_opsr__df_evls__df_evl__df_mhp__df_psd__df_selv__df_algind__df_psr1__df_vr1__df_ply1__df_coe1__df_toply1__df_evls1__df_evl1__df_psmet__df_xmet : ∀ x0 : ο . (wceq cmpl (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (co (cv x1) (cv x2) cmps) (λ x3 . co (cv x3) (crab (λ x4 . wbr (cv x4) (cfv (cv x2) c0g) cfsupp) (λ x4 . cfv (cv x3) cbs)) cress))) ⟶ wceq cltb (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . copab (λ x3 x4 . wa (wss (cpr (cv x3) (cv x4)) (crab (λ x5 . wcel (cima (ccnv (cv x5)) cn) cfn) (λ x5 . co cn0 (cv x2) cmap))) (wrex (λ x5 . wa (wbr (cfv (cv x5) (cv x3)) (cfv (cv x5) (cv x4)) clt) (wral (λ x6 . wbr (cv x5) (cv x6) (cv x1) ⟶ wceq (cfv (cv x6) (cv x3)) (cfv (cv x6) (cv x4))) (λ x6 . cv x2))) (λ x5 . cv x2))))) ⟶ wceq copws (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cpw (cxp (cv x1) (cv x1))) (λ x3 . csb (co (cv x1) (cv x2) cmps) (λ x4 . co (cv x4) (cop (cfv cnx cple) (copab (λ x5 x6 . wa (wss (cpr (cv x5) (cv x6)) (cfv (cv x4) cbs)) (wo (wsbc (λ x7 . wrex (λ x8 . wa (wbr (cfv (cv x8) (cv x5)) (cfv (cv x8) (cv x6)) (cfv (cv x2) cplt)) (wral (λ x9 . wbr (cv x9) (cv x8) (co (cv x3) (cv x1) cltb) ⟶ wceq (cfv (cv x9) (cv x5)) (cfv (cv x9) (cv x6))) (λ x9 . cv x7))) (λ x8 . cv x7)) (crab (λ x7 . wcel (cima (ccnv (cv x7)) cn) cfn) (λ x7 . co cn0 (cv x1) cmap))) (wceq (cv x5) (cv x6)))))) csts)))) ⟶ wceq ces (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . ccrg) (λ x1 x2 . csb (cfv (cv x2) cbs) (λ x3 . cmpt (λ x4 . cfv (cv x2) csubrg) (λ x4 . csb (co (cv x1) (co (cv x2) (cv x4) cress) cmpl) (λ x5 . crio (λ x6 . wa (wceq (ccom (cv x6) (cfv (cv x5) cascl)) (cmpt (λ x7 . cv x4) (λ x7 . cxp (co (cv x3) (cv x1) cmap) (csn (cv x7))))) (wceq (ccom (cv x6) (co (cv x1) (co (cv x2) (cv x4) cress) cmvr)) (cmpt (λ x7 . cv x1) (λ x7 . cmpt (λ x8 . co (cv x3) (cv x1) cmap) (λ x8 . cfv (cv x7) (cv x8)))))) (λ x6 . co (cv x5) (co (cv x2) (co (cv x3) (cv x1) cmap) cpws) crh)))))) ⟶ wceq cevl (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cfv (cfv (cv x2) cbs) (co (cv x1) (cv x2) ces))) ⟶ wceq cmhp (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cn0) (λ x3 . crab (λ x4 . wss (co (cv x4) (cfv (cv x2) c0g) csupp) (crab (λ x5 . wceq (csu cn0 (λ x6 . cfv (cv x6) (cv x5))) (cv x3)) (λ x5 . crab (λ x6 . wcel (cima (ccnv (cv x6)) cn) cfn) (λ x6 . co cn0 (cv x1) cmap)))) (λ x4 . cfv (co (cv x1) (cv x2) cmpl) cbs)))) ⟶ wceq cpsd (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cv x1) (λ x3 . cmpt (λ x4 . cfv (co (cv x1) (cv x2) cmps) cbs) (λ x4 . cmpt (λ x5 . crab (λ x6 . wcel (cima (ccnv (cv x6)) cn) cfn) (λ x6 . co cn0 (cv x1) cmap)) (λ x5 . co (co (cfv (cv x3) (cv x5)) c1 caddc) (cfv (co (cv x5) (cmpt (λ x6 . cv x1) (λ x6 . cif (wceq (cv x6) (cv x3)) c1 cc0)) (cof caddc)) (cv x4)) (cfv (cv x2) cmg)))))) ⟶ wceq cslv (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cpw (cv x1)) (λ x3 . cmpt (λ x4 . co (cv x1) (cv x2) cmpl) (λ x4 . csb (co (cdif (cv x1) (cv x3)) (cv x2) cmpl) (λ x5 . csb (cmpt (λ x6 . cfv (cv x5) csca) (λ x6 . co (cv x6) (cfv (cv x5) cur) (cfv (cv x5) cvsca))) (λ x6 . cfv (cmpt (λ x7 . cv x1) (λ x7 . cif (wcel (cv x7) (cv x3)) (cfv (cv x7) (co (cv x3) (co (cdif (cv x1) (cv x3)) (cv x2) cmpl) cmvr)) (ccom (cv x6) (cfv (cv x7) (co (cdif (cv x1) (cv x3)) (cv x2) cmvr))))) (cfv (ccom (cv x6) (cv x4)) (cfv (co (cv x6) (cv x2) cimas) (co (cv x1) (cv x5) ces))))))))) ⟶ wceq cai (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cpw (cfv (cv x1) cbs)) (λ x1 x2 . crab (λ x3 . wfun (ccnv (cmpt (λ x4 . cfv (co (cv x3) (co (cv x1) (cv x2) cress) cmpl) cbs) (λ x4 . cfv (cres cid (cv x3)) (cfv (cv x4) (cfv (cv x2) (co (cv x3) (cv x1) ces))))))) (λ x3 . cpw (cfv (cv x1) cbs)))) ⟶ wceq cps1 (cmpt (λ x1 . cvv) (λ x1 . cfv c0 (co c1o (cv x1) copws))) ⟶ wceq cv1 (cmpt (λ x1 . cvv) (λ x1 . cfv c0 (co c1o (cv x1) cmvr))) ⟶ wceq cpl1 (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cv x1) cps1) (cfv (co c1o (cv x1) cmpl) cbs) cress)) ⟶ wceq cco1 (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cn0) (λ x2 . cfv (cxp c1o (csn (cv x2))) (cv x1)))) ⟶ wceq ctp1 (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . co cn0 c1o cmap) (λ x2 . cfv (cfv c0 (cv x2)) (cv x1)))) ⟶ wceq ces1 (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cpw (cfv (cv x1) cbs)) (λ x1 x2 . csb (cfv (cv x1) cbs) (λ x3 . ccom (cmpt (λ x4 . co (cv x3) (co (cv x3) c1o cmap) cmap) (λ x4 . ccom (cv x4) (cmpt (λ x5 . cv x3) (λ x5 . cxp c1o (csn (cv x5)))))) (cfv (cv x2) (co c1o (cv x1) ces))))) ⟶ wceq ce1 (cmpt (λ x1 . cvv) (λ x1 . csb (cfv (cv x1) cbs) (λ x2 . ccom (cmpt (λ x3 . co (cv x2) (co (cv x2) c1o cmap) cmap) (λ x3 . ccom (cv x3) (cmpt (λ x4 . cv x2) (λ x4 . cxp c1o (csn (cv x4)))))) (co c1o (cv x1) cevl)))) ⟶ wceq cpsmet (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wa (wceq (co (cv x3) (cv x3) (cv x2)) cc0) (wral (λ x4 . wral (λ x5 . wbr (co (cv x3) (cv x4) (cv x2)) (co (co (cv x5) (cv x3) (cv x2)) (co (cv x5) (cv x4) (cv x2)) cxad) cle) (λ x5 . cv x1)) (λ x4 . cv x1))) (λ x3 . cv x1)) (λ x2 . co cxr (cxp (cv x1) (cv x1)) cmap))) ⟶ wceq cxmt (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wral (λ x4 . wa (wb (wceq (co (cv x3) (cv x4) (cv x2)) cc0) (wceq (cv x3) (cv x4))) (wral (λ x5 . wbr (co (cv x3) (cv x4) (cv x2)) (co (co (cv x5) (cv x3) (cv x2)) (co (cv x5) (cv x4) (cv x2)) cxad) cle) (λ x5 . cv x1))) (λ x4 . cv x1)) (λ x3 . cv x1)) (λ x2 . co cxr (cxp (cv x1) (cv x1)) cmap))) ⟶ x0) ⟶ x0
Axiom df_met__df_bl__df_mopn__df_fbas__df_fg__df_metu__df_cnfld__df_zring__df_zrh__df_zlm__df_chr__df_zn__df_refld__df_phl__df_ipf__df_ocv__df_css__df_thl : ∀ x0 : ο . (wceq cme (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wral (λ x4 . wa (wb (wceq (co (cv x3) (cv x4) (cv x2)) cc0) (wceq (cv x3) (cv x4))) (wral (λ x5 . wbr (co (cv x3) (cv x4) (cv x2)) (co (co (cv x5) (cv x3) (cv x2)) (co (cv x5) (cv x4) (cv x2)) caddc) cle) (λ x5 . cv x1))) (λ x4 . cv x1)) (λ x3 . cv x1)) (λ x2 . co cr (cxp (cv x1) (cv x1)) cmap))) ⟶ wceq cbl (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cdm (cdm (cv x1))) (λ x2 x3 . cxr) (λ x2 x3 . crab (λ x4 . wbr (co (cv x2) (cv x4) (cv x1)) (cv x3) clt) (λ x4 . cdm (cdm (cv x1)))))) ⟶ wceq cmopn (cmpt (λ x1 . cuni (crn cxmt)) (λ x1 . cfv (crn (cfv (cv x1) cbl)) ctg)) ⟶ wceq cfbas (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . w3a (wne (cv x2) c0) (wnel c0 (cv x2)) (wral (λ x3 . wral (λ x4 . wne (cin (cv x2) (cpw (cin (cv x3) (cv x4)))) c0) (λ x4 . cv x2)) (λ x3 . cv x2))) (λ x2 . cpw (cpw (cv x1))))) ⟶ wceq cfg (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cfv (cv x1) cfbas) (λ x1 x2 . crab (λ x3 . wne (cin (cv x2) (cpw (cv x3))) c0) (λ x3 . cpw (cv x1)))) ⟶ wceq cmetu (cmpt (λ x1 . cuni (crn cpsmet)) (λ x1 . co (cxp (cdm (cdm (cv x1))) (cdm (cdm (cv x1)))) (crn (cmpt (λ x2 . crp) (λ x2 . cima (ccnv (cv x1)) (co cc0 (cv x2) cico)))) cfg)) ⟶ wceq ccnfld (cun (cun (ctp (cop (cfv cnx cbs) cc) (cop (cfv cnx cplusg) caddc) (cop (cfv cnx cmulr) cmul)) (csn (cop (cfv cnx cstv) ccj))) (cun (ctp (cop (cfv cnx cts) (cfv (ccom cabs cmin) cmopn)) (cop (cfv cnx cple) cle) (cop (cfv cnx cds) (ccom cabs cmin))) (csn (cop (cfv cnx cunif) (cfv (ccom cabs cmin) cmetu))))) ⟶ wceq zring (co ccnfld cz cress) ⟶ wceq czrh (cmpt (λ x1 . cvv) (λ x1 . cuni (co zring (cv x1) crh))) ⟶ wceq czlm (cmpt (λ x1 . cvv) (λ x1 . co (co (cv x1) (cop (cfv cnx csca) zring) csts) (cop (cfv cnx cvsca) (cfv (cv x1) cmg)) csts)) ⟶ wceq cchr (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cur) (cfv (cv x1) cod))) ⟶ wceq czn (cmpt (λ x1 . cn0) (λ x1 . csb zring (λ x2 . csb (co (cv x2) (co (cv x2) (cfv (csn (cv x1)) (cfv (cv x2) crsp)) cqg) cqus) (λ x3 . co (cv x3) (cop (cfv cnx cple) (csb (cres (cfv (cv x3) czrh) (cif (wceq (cv x1) cc0) cz (co cc0 (cv x1) cfzo))) (λ x4 . ccom (ccom (cv x4) cle) (ccnv (cv x4))))) csts)))) ⟶ wceq crefld (co ccnfld cr cress) ⟶ wceq cphl (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wa (wcel (cv x4) csr) (wral (λ x5 . w3a (wcel (cmpt (λ x6 . cv x2) (λ x6 . co (cv x6) (cv x5) (cv x3))) (co (cv x1) (cfv (cv x4) crglmod) clmhm)) (wceq (co (cv x5) (cv x5) (cv x3)) (cfv (cv x4) c0g) ⟶ wceq (cv x5) (cfv (cv x1) c0g)) (wral (λ x6 . wceq (cfv (co (cv x5) (cv x6) (cv x3)) (cfv (cv x4) cstv)) (co (cv x6) (cv x5) (cv x3))) (λ x6 . cv x2))) (λ x5 . cv x2))) (cfv (cv x1) csca)) (cfv (cv x1) cip)) (cfv (cv x1) cbs)) (λ x1 . clvec)) ⟶ wceq cipf (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . co (cv x2) (cv x3) (cfv (cv x1) cip)))) ⟶ wceq cocv (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) cbs)) (λ x2 . crab (λ x3 . wral (λ x4 . wceq (co (cv x3) (cv x4) (cfv (cv x1) cip)) (cfv (cfv (cv x1) csca) c0g)) (λ x4 . cv x2)) (λ x3 . cfv (cv x1) cbs)))) ⟶ wceq ccss (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wceq (cv x2) (cfv (cfv (cv x2) (cfv (cv x1) cocv)) (cfv (cv x1) cocv))))) ⟶ wceq cthl (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cfv (cv x1) ccss) cipo) (cop (cfv cnx coc) (cfv (cv x1) cocv)) csts)) ⟶ x0) ⟶ x0
Axiom df_pj__df_hil__df_obs__df_dsmm__df_frlm__df_uvc__df_lindf__df_linds__df_mamu__df_mat__df_dmat__df_scmat__df_mvmul__df_marrep__df_marepv__df_subma__df_mdet__df_madu : ∀ x0 : ο . (wceq cpj (cmpt (λ x1 . cvv) (λ x1 . cin (cmpt (λ x2 . cfv (cv x1) clss) (λ x2 . co (cv x2) (cfv (cv x2) (cfv (cv x1) cocv)) (cfv (cv x1) cpj1))) (cxp cvv (co (cfv (cv x1) cbs) (cfv (cv x1) cbs) cmap)))) ⟶ wceq chs (crab (λ x1 . wceq (cdm (cfv (cv x1) cpj)) (cfv (cv x1) ccss)) (λ x1 . cphl)) ⟶ wceq cobs (cmpt (λ x1 . cphl) (λ x1 . crab (λ x2 . wa (wral (λ x3 . wral (λ x4 . wceq (co (cv x3) (cv x4) (cfv (cv x1) cip)) (cif (wceq (cv x3) (cv x4)) (cfv (cfv (cv x1) csca) cur) (cfv (cfv (cv x1) csca) c0g))) (λ x4 . cv x2)) (λ x3 . cv x2)) (wceq (cfv (cv x2) (cfv (cv x1) cocv)) (csn (cfv (cv x1) c0g)))) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq cdsmm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cv x1) (cv x2) cprds) (crab (λ x3 . wcel (crab (λ x4 . wne (cfv (cv x4) (cv x3)) (cfv (cfv (cv x4) (cv x2)) c0g)) (λ x4 . cdm (cv x2))) cfn) (λ x3 . cixp (λ x4 . cdm (cv x2)) (λ x4 . cfv (cfv (cv x4) (cv x2)) cbs))) cress)) ⟶ wceq cfrlm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cv x1) (cxp (cv x2) (csn (cfv (cv x1) crglmod))) cdsmm)) ⟶ wceq cuvc (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cv x2) (λ x3 . cmpt (λ x4 . cv x2) (λ x4 . cif (wceq (cv x4) (cv x3)) (cfv (cv x1) cur) (cfv (cv x1) c0g))))) ⟶ wceq clindf (copab (λ x1 x2 . wa (wf (cdm (cv x1)) (cfv (cv x2) cbs) (cv x1)) (wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wn (wcel (co (cv x5) (cfv (cv x4) (cv x1)) (cfv (cv x2) cvsca)) (cfv (cima (cv x1) (cdif (cdm (cv x1)) (csn (cv x4)))) (cfv (cv x2) clspn)))) (λ x5 . cdif (cfv (cv x3) cbs) (csn (cfv (cv x3) c0g)))) (λ x4 . cdm (cv x1))) (cfv (cv x2) csca)))) ⟶ wceq clinds (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cres cid (cv x2)) (cv x1) clindf) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq cmmul (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cfv (cv x2) c1st) c1st) (λ x3 . csb (cfv (cfv (cv x2) c1st) c2nd) (λ x4 . csb (cfv (cv x2) c2nd) (λ x5 . cmpt2 (λ x6 x7 . co (cfv (cv x1) cbs) (cxp (cv x3) (cv x4)) cmap) (λ x6 x7 . co (cfv (cv x1) cbs) (cxp (cv x4) (cv x5)) cmap) (λ x6 x7 . cmpt2 (λ x8 x9 . cv x3) (λ x8 x9 . cv x5) (λ x8 x9 . co (cv x1) (cmpt (λ x10 . cv x4) (λ x10 . co (co (cv x8) (cv x10) (cv x6)) (co (cv x10) (cv x9) (cv x7)) (cfv (cv x1) cmulr))) cgsu))))))) ⟶ wceq cmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cv x2) (cxp (cv x1) (cv x1)) cfrlm) (cop (cfv cnx cmulr) (co (cv x2) (cotp (cv x1) (cv x1) (cv x1)) cmmul)) csts)) ⟶ wceq cdmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wne (cv x4) (cv x5) ⟶ wceq (co (cv x4) (cv x5) (cv x3)) (cfv (cv x2) c0g)) (λ x5 . cv x1)) (λ x4 . cv x1)) (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs))) ⟶ wceq cscmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . csb (co (cv x1) (cv x2) cmat) (λ x3 . crab (λ x4 . wrex (λ x5 . wceq (cv x4) (co (cv x5) (cfv (cv x3) cur) (cfv (cv x3) cvsca))) (λ x5 . cfv (cv x2) cbs)) (λ x4 . cfv (cv x3) cbs)))) ⟶ wceq cmvmul (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x2) c1st) (λ x3 . csb (cfv (cv x2) c2nd) (λ x4 . cmpt2 (λ x5 x6 . co (cfv (cv x1) cbs) (cxp (cv x3) (cv x4)) cmap) (λ x5 x6 . co (cfv (cv x1) cbs) (cv x4) cmap) (λ x5 x6 . cmpt (λ x7 . cv x3) (λ x7 . co (cv x1) (cmpt (λ x8 . cv x4) (λ x8 . co (co (cv x7) (cv x8) (cv x5)) (cfv (cv x8) (cv x6)) (cfv (cv x1) cmulr))) cgsu)))))) ⟶ wceq cmarrep (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt2 (λ x3 x4 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 x4 . cfv (cv x2) cbs) (λ x3 x4 . cmpt2 (λ x5 x6 . cv x1) (λ x5 x6 . cv x1) (λ x5 x6 . cmpt2 (λ x7 x8 . cv x1) (λ x7 x8 . cv x1) (λ x7 x8 . cif (wceq (cv x7) (cv x5)) (cif (wceq (cv x8) (cv x6)) (cv x4) (cfv (cv x2) c0g)) (co (cv x7) (cv x8) (cv x3))))))) ⟶ wceq cmatrepV (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt2 (λ x3 x4 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 x4 . co (cfv (cv x2) cbs) (cv x1) cmap) (λ x3 x4 . cmpt (λ x5 . cv x1) (λ x5 . cmpt2 (λ x6 x7 . cv x1) (λ x6 x7 . cv x1) (λ x6 x7 . cif (wceq (cv x7) (cv x5)) (cfv (cv x6) (cv x4)) (co (cv x6) (cv x7) (cv x3))))))) ⟶ wceq csubma (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . cmpt2 (λ x4 x5 . cv x1) (λ x4 x5 . cv x1) (λ x4 x5 . cmpt2 (λ x6 x7 . cdif (cv x1) (csn (cv x4))) (λ x6 x7 . cdif (cv x1) (csn (cv x5))) (λ x6 x7 . co (cv x6) (cv x7) (cv x3)))))) ⟶ wceq cmdat (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . co (cv x2) (cmpt (λ x4 . cfv (cfv (cv x1) csymg) cbs) (λ x4 . co (cfv (cv x4) (ccom (cfv (cv x2) czrh) (cfv (cv x1) cpsgn))) (co (cfv (cv x2) cmgp) (cmpt (λ x5 . cv x1) (λ x5 . co (cfv (cv x5) (cv x4)) (cv x5) (cv x3))) cgsu) (cfv (cv x2) cmulr))) cgsu))) ⟶ wceq cmadu (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . cmpt2 (λ x4 x5 . cv x1) (λ x4 x5 . cv x1) (λ x4 x5 . cfv (cmpt2 (λ x6 x7 . cv x1) (λ x6 x7 . cv x1) (λ x6 x7 . cif (wceq (cv x6) (cv x5)) (cif (wceq (cv x7) (cv x4)) (cfv (cv x2) cur) (cfv (cv x2) c0g)) (co (cv x6) (cv x7) (cv x3)))) (co (cv x1) (cv x2) cmdat))))) ⟶ x0) ⟶ x0
Axiom df_minmar1__df_cpmat__df_mat2pmat__df_cpmat2mat__df_decpmat__df_pm2mp__df_chpmat__df_top__df_topon__df_topsp__df_bases__df_cld__df_ntr__df_cls__df_nei__df_lp__df_perf__df_cn : ∀ x0 : ο . (wceq cminmar1 (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . cmpt2 (λ x4 x5 . cv x1) (λ x4 x5 . cv x1) (λ x4 x5 . cmpt2 (λ x6 x7 . cv x1) (λ x6 x7 . cv x1) (λ x6 x7 . cif (wceq (cv x6) (cv x4)) (cif (wceq (cv x7) (cv x5)) (cfv (cv x2) cur) (cfv (cv x2) c0g)) (co (cv x6) (cv x7) (cv x3))))))) ⟶ wceq ccpmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wceq (cfv (cv x6) (cfv (co (cv x4) (cv x5) (cv x3)) cco1)) (cfv (cv x2) c0g)) (λ x6 . cn)) (λ x5 . cv x1)) (λ x4 . cv x1)) (λ x3 . cfv (co (cv x1) (cfv (cv x2) cpl1) cmat) cbs))) ⟶ wceq cmat2pmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . cmpt2 (λ x4 x5 . cv x1) (λ x4 x5 . cv x1) (λ x4 x5 . cfv (co (cv x4) (cv x5) (cv x3)) (cfv (cfv (cv x2) cpl1) cascl))))) ⟶ wceq ccpmat2mat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . co (cv x1) (cv x2) ccpmat) (λ x3 . cmpt2 (λ x4 x5 . cv x1) (λ x4 x5 . cv x1) (λ x4 x5 . cfv cc0 (cfv (co (cv x4) (cv x5) (cv x3)) cco1))))) ⟶ wceq cdecpmat (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cn0) (λ x1 x2 . cmpt2 (λ x3 x4 . cdm (cdm (cv x1))) (λ x3 x4 . cdm (cdm (cv x1))) (λ x3 x4 . cfv (cv x2) (cfv (co (cv x3) (cv x4) (cv x1)) cco1)))) ⟶ wceq cpm2mp (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cfv (cv x2) cpl1) cmat) cbs) (λ x3 . csb (co (cv x1) (cv x2) cmat) (λ x4 . csb (cfv (cv x4) cpl1) (λ x5 . co (cv x5) (cmpt (λ x6 . cn0) (λ x6 . co (co (cv x3) (cv x6) cdecpmat) (co (cv x6) (cfv (cv x4) cv1) (cfv (cfv (cv x5) cmgp) cmg)) (cfv (cv x5) cvsca))) cgsu))))) ⟶ wceq cchpmat (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmat) cbs) (λ x3 . cfv (co (co (cfv (cv x2) cv1) (cfv (co (cv x1) (cfv (cv x2) cpl1) cmat) cur) (cfv (co (cv x1) (cfv (cv x2) cpl1) cmat) cvsca)) (cfv (cv x3) (co (cv x1) (cv x2) cmat2pmat)) (cfv (co (cv x1) (cfv (cv x2) cpl1) cmat) csg)) (co (cv x1) (cfv (cv x2) cpl1) cmdat)))) ⟶ wceq ctop (cab (λ x1 . wa (wral (λ x2 . wcel (cuni (cv x2)) (cv x1)) (λ x2 . cpw (cv x1))) (wral (λ x2 . wral (λ x3 . wcel (cin (cv x2) (cv x3)) (cv x1)) (λ x3 . cv x1)) (λ x2 . cv x1)))) ⟶ wceq ctopon (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wceq (cv x1) (cuni (cv x2))) (λ x2 . ctop))) ⟶ wceq ctps (cab (λ x1 . wcel (cfv (cv x1) ctopn) (cfv (cfv (cv x1) cbs) ctopon))) ⟶ wceq ctb (cab (λ x1 . wral (λ x2 . wral (λ x3 . wss (cin (cv x2) (cv x3)) (cuni (cin (cv x1) (cpw (cin (cv x2) (cv x3)))))) (λ x3 . cv x1)) (λ x2 . cv x1))) ⟶ wceq ccld (cmpt (λ x1 . ctop) (λ x1 . crab (λ x2 . wcel (cdif (cuni (cv x1)) (cv x2)) (cv x1)) (λ x2 . cpw (cuni (cv x1))))) ⟶ wceq cnt (cmpt (λ x1 . ctop) (λ x1 . cmpt (λ x2 . cpw (cuni (cv x1))) (λ x2 . cuni (cin (cv x1) (cpw (cv x2)))))) ⟶ wceq ccl (cmpt (λ x1 . ctop) (λ x1 . cmpt (λ x2 . cpw (cuni (cv x1))) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) ccld))))) ⟶ wceq cnei (cmpt (λ x1 . ctop) (λ x1 . cmpt (λ x2 . cpw (cuni (cv x1))) (λ x2 . crab (λ x3 . wrex (λ x4 . wa (wss (cv x2) (cv x4)) (wss (cv x4) (cv x3))) (λ x4 . cv x1)) (λ x3 . cpw (cuni (cv x1)))))) ⟶ wceq clp (cmpt (λ x1 . ctop) (λ x1 . cmpt (λ x2 . cpw (cuni (cv x1))) (λ x2 . cab (λ x3 . wcel (cv x3) (cfv (cdif (cv x2) (csn (cv x3))) (cfv (cv x1) ccl)))))) ⟶ wceq cperf (crab (λ x1 . wceq (cfv (cuni (cv x1)) (cfv (cv x1) clp)) (cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq ccn (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wcel (cima (ccnv (cv x3)) (cv x4)) (cv x1)) (λ x4 . cv x2)) (λ x3 . co (cuni (cv x2)) (cuni (cv x1)) cmap))) ⟶ x0) ⟶ x0
Axiom df_cnp__df_lm__df_t0__df_t1__df_haus__df_reg__df_nrm__df_cnrm__df_pnrm__df_cmp__df_conn__df_1stc__df_2ndc__df_lly__df_nlly__df_ref__df_ptfin__df_locfin : ∀ x0 : ο . (wceq ccnp (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . cmpt (λ x3 . cuni (cv x1)) (λ x3 . crab (λ x4 . wral (λ x5 . wcel (cfv (cv x3) (cv x4)) (cv x5) ⟶ wrex (λ x6 . wa (wcel (cv x3) (cv x6)) (wss (cima (cv x4) (cv x6)) (cv x5))) (λ x6 . cv x1)) (λ x5 . cv x2)) (λ x4 . co (cuni (cv x2)) (cuni (cv x1)) cmap)))) ⟶ wceq clm (cmpt (λ x1 . ctop) (λ x1 . copab (λ x2 x3 . w3a (wcel (cv x2) (co (cuni (cv x1)) cc cpm)) (wcel (cv x3) (cuni (cv x1))) (wral (λ x4 . wcel (cv x3) (cv x4) ⟶ wrex (λ x5 . wf (cv x5) (cv x4) (cres (cv x2) (cv x5))) (λ x5 . crn cuz)) (λ x4 . cv x1))))) ⟶ wceq ct0 (crab (λ x1 . wral (λ x2 . wral (λ x3 . wral (λ x4 . wb (wcel (cv x2) (cv x4)) (wcel (cv x3) (cv x4))) (λ x4 . cv x1) ⟶ wceq (cv x2) (cv x3)) (λ x3 . cuni (cv x1))) (λ x2 . cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq ct1 (crab (λ x1 . wral (λ x2 . wcel (csn (cv x2)) (cfv (cv x1) ccld)) (λ x2 . cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq cha (crab (λ x1 . wral (λ x2 . wral (λ x3 . wne (cv x2) (cv x3) ⟶ wrex (λ x4 . wrex (λ x5 . w3a (wcel (cv x2) (cv x4)) (wcel (cv x3) (cv x5)) (wceq (cin (cv x4) (cv x5)) c0)) (λ x5 . cv x1)) (λ x4 . cv x1)) (λ x3 . cuni (cv x1))) (λ x2 . cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq creg (crab (λ x1 . wral (λ x2 . wral (λ x3 . wrex (λ x4 . wa (wcel (cv x3) (cv x4)) (wss (cfv (cv x4) (cfv (cv x1) ccl)) (cv x2))) (λ x4 . cv x1)) (λ x3 . cv x2)) (λ x2 . cv x1)) (λ x1 . ctop)) ⟶ wceq cnrm (crab (λ x1 . wral (λ x2 . wral (λ x3 . wrex (λ x4 . wa (wss (cv x3) (cv x4)) (wss (cfv (cv x4) (cfv (cv x1) ccl)) (cv x2))) (λ x4 . cv x1)) (λ x3 . cin (cfv (cv x1) ccld) (cpw (cv x2)))) (λ x2 . cv x1)) (λ x1 . ctop)) ⟶ wceq ccnrm (crab (λ x1 . wral (λ x2 . wcel (co (cv x1) (cv x2) crest) cnrm) (λ x2 . cpw (cuni (cv x1)))) (λ x1 . ctop)) ⟶ wceq cpnrm (crab (λ x1 . wss (cfv (cv x1) ccld) (crn (cmpt (λ x2 . co (cv x1) cn cmap) (λ x2 . cint (crn (cv x2)))))) (λ x1 . cnrm)) ⟶ wceq ccmp (crab (λ x1 . wral (λ x2 . wceq (cuni (cv x1)) (cuni (cv x2)) ⟶ wrex (λ x3 . wceq (cuni (cv x1)) (cuni (cv x3))) (λ x3 . cin (cpw (cv x2)) cfn)) (λ x2 . cpw (cv x1))) (λ x1 . ctop)) ⟶ wceq cconn (crab (λ x1 . wceq (cin (cv x1) (cfv (cv x1) ccld)) (cpr c0 (cuni (cv x1)))) (λ x1 . ctop)) ⟶ wceq c1stc (crab (λ x1 . wral (λ x2 . wrex (λ x3 . wa (wbr (cv x3) com cdom) (wral (λ x4 . wcel (cv x2) (cv x4) ⟶ wcel (cv x2) (cuni (cin (cv x3) (cpw (cv x4))))) (λ x4 . cv x1))) (λ x3 . cpw (cv x1))) (λ x2 . cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq c2ndc (cab (λ x1 . wrex (λ x2 . wa (wbr (cv x2) com cdom) (wceq (cfv (cv x2) ctg) (cv x1))) (λ x2 . ctb))) ⟶ (∀ x1 : ι → ο . wceq (clly x1) (crab (λ x2 . wral (λ x3 . wral (λ x4 . wrex (λ x5 . wa (wcel (cv x4) (cv x5)) (wcel (co (cv x2) (cv x5) crest) x1)) (λ x5 . cin (cv x2) (cpw (cv x3)))) (λ x4 . cv x3)) (λ x3 . cv x2)) (λ x2 . ctop))) ⟶ (∀ x1 : ι → ο . wceq (cnlly x1) (crab (λ x2 . wral (λ x3 . wral (λ x4 . wrex (λ x5 . wcel (co (cv x2) (cv x5) crest) x1) (λ x5 . cin (cfv (csn (cv x4)) (cfv (cv x2) cnei)) (cpw (cv x3)))) (λ x4 . cv x3)) (λ x3 . cv x2)) (λ x2 . ctop))) ⟶ wceq cref (copab (λ x1 x2 . wa (wceq (cuni (cv x2)) (cuni (cv x1))) (wral (λ x3 . wrex (λ x4 . wss (cv x3) (cv x4)) (λ x4 . cv x2)) (λ x3 . cv x1)))) ⟶ wceq cptfin (cab (λ x1 . wral (λ x2 . wcel (crab (λ x3 . wcel (cv x2) (cv x3)) (λ x3 . cv x1)) cfn) (λ x2 . cuni (cv x1)))) ⟶ wceq clocfin (cmpt (λ x1 . ctop) (λ x1 . cab (λ x2 . wa (wceq (cuni (cv x1)) (cuni (cv x2))) (wral (λ x3 . wrex (λ x4 . wa (wcel (cv x3) (cv x4)) (wcel (crab (λ x5 . wne (cin (cv x5) (cv x4)) c0) (λ x5 . cv x2)) cfn)) (λ x4 . cv x1)) (λ x3 . cuni (cv x1)))))) ⟶ x0) ⟶ x0
Axiom df_kgen__df_tx__df_xko__df_kq__df_hmeo__df_hmph__df_fil__df_ufil__df_ufl__df_fm__df_flim__df_flf__df_fcls__df_fcf__df_cnext__df_tmd__df_tgp__df_tsms : ∀ x0 : ο . (wceq ckgen (cmpt (λ x1 . ctop) (λ x1 . crab (λ x2 . wral (λ x3 . wcel (co (cv x1) (cv x3) crest) ccmp ⟶ wcel (cin (cv x2) (cv x3)) (co (cv x1) (cv x3) crest)) (λ x3 . cpw (cuni (cv x1)))) (λ x2 . cpw (cuni (cv x1))))) ⟶ wceq ctx (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cfv (crn (cmpt2 (λ x3 x4 . cv x1) (λ x3 x4 . cv x2) (λ x3 x4 . cxp (cv x3) (cv x4)))) ctg)) ⟶ wceq cxko (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . cfv (cfv (crn (cmpt2 (λ x3 x4 . crab (λ x5 . wcel (co (cv x2) (cv x5) crest) ccmp) (λ x5 . cpw (cuni (cv x2)))) (λ x3 x4 . cv x1) (λ x3 x4 . crab (λ x5 . wss (cima (cv x5) (cv x3)) (cv x4)) (λ x5 . co (cv x2) (cv x1) ccn)))) cfi) ctg)) ⟶ wceq ckq (cmpt (λ x1 . ctop) (λ x1 . co (cv x1) (cmpt (λ x2 . cuni (cv x1)) (λ x2 . crab (λ x3 . wcel (cv x2) (cv x3)) (λ x3 . cv x1))) cqtop)) ⟶ wceq chmeo (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . crab (λ x3 . wcel (ccnv (cv x3)) (co (cv x2) (cv x1) ccn)) (λ x3 . co (cv x1) (cv x2) ccn))) ⟶ wceq chmph (cima (ccnv chmeo) (cdif cvv c1o)) ⟶ wceq cfil (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wne (cin (cv x2) (cpw (cv x3))) c0 ⟶ wcel (cv x3) (cv x2)) (λ x3 . cpw (cv x1))) (λ x2 . cfv (cv x1) cfbas))) ⟶ wceq cufil (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wo (wcel (cv x3) (cv x2)) (wcel (cdif (cv x1) (cv x3)) (cv x2))) (λ x3 . cpw (cv x1))) (λ x2 . cfv (cv x1) cfil))) ⟶ wceq cufl (cab (λ x1 . wral (λ x2 . wrex (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) cufil)) (λ x2 . cfv (cv x1) cfil))) ⟶ wceq cfm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (cdm (cv x2)) cfbas) (λ x3 . co (cv x1) (crn (cmpt (λ x4 . cv x3) (λ x4 . cima (cv x2) (cv x4)))) cfg))) ⟶ wceq cflim (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (crn cfil)) (λ x1 x2 . crab (λ x3 . wa (wss (cfv (csn (cv x3)) (cfv (cv x1) cnei)) (cv x2)) (wss (cv x2) (cpw (cuni (cv x1))))) (λ x3 . cuni (cv x1)))) ⟶ wceq cflf (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (crn cfil)) (λ x1 x2 . cmpt (λ x3 . co (cuni (cv x1)) (cuni (cv x2)) cmap) (λ x3 . co (cv x1) (cfv (cv x2) (co (cuni (cv x1)) (cv x3) cfm)) cflim))) ⟶ wceq cfcls (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (crn cfil)) (λ x1 x2 . cif (wceq (cuni (cv x1)) (cuni (cv x2))) (ciin (λ x3 . cv x2) (λ x3 . cfv (cv x3) (cfv (cv x1) ccl))) c0)) ⟶ wceq cfcf (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (crn cfil)) (λ x1 x2 . cmpt (λ x3 . co (cuni (cv x1)) (cuni (cv x2)) cmap) (λ x3 . co (cv x1) (cfv (cv x2) (co (cuni (cv x1)) (cv x3) cfm)) cfcls))) ⟶ wceq ccnext (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . cmpt (λ x3 . co (cuni (cv x2)) (cuni (cv x1)) cpm) (λ x3 . ciun (λ x4 . cfv (cdm (cv x3)) (cfv (cv x1) ccl)) (λ x4 . cxp (csn (cv x4)) (cfv (cv x3) (co (cv x2) (co (cfv (csn (cv x4)) (cfv (cv x1) cnei)) (cdm (cv x3)) crest) cflf)))))) ⟶ wceq ctmd (crab (λ x1 . wsbc (λ x2 . wcel (cfv (cv x1) cplusf) (co (co (cv x2) (cv x2) ctx) (cv x2) ccn)) (cfv (cv x1) ctopn)) (λ x1 . cin cmnd ctps)) ⟶ wceq ctgp (crab (λ x1 . wsbc (λ x2 . wcel (cfv (cv x1) cminusg) (co (cv x2) (cv x2) ccn)) (cfv (cv x1) ctopn)) (λ x1 . cin cgrp ctmd)) ⟶ wceq ctsu (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cin (cpw (cdm (cv x2))) cfn) (λ x3 . cfv (cmpt (λ x4 . cv x3) (λ x4 . co (cv x1) (cres (cv x2) (cv x4)) cgsu)) (co (cfv (cv x1) ctopn) (co (cv x3) (crn (cmpt (λ x4 . cv x3) (λ x4 . crab (λ x5 . wss (cv x4) (cv x5)) (λ x5 . cv x3)))) cfg) cflf)))) ⟶ x0) ⟶ x0
Axiom df_trg__df_tdrg__df_tlm__df_tvc__df_ust__df_utop__df_uss__df_usp__df_tus__df_ucn__df_cfilu__df_cusp__df_xms__df_ms__df_tms__df_nm__df_ngp__df_tng : ∀ x0 : ο . (wceq ctrg (crab (λ x1 . wcel (cfv (cv x1) cmgp) ctmd) (λ x1 . cin ctgp crg)) ⟶ wceq ctdrg (crab (λ x1 . wcel (co (cfv (cv x1) cmgp) (cfv (cv x1) cui) cress) ctgp) (λ x1 . cin ctrg cdr)) ⟶ wceq ctlm (crab (λ x1 . wa (wcel (cfv (cv x1) csca) ctrg) (wcel (cfv (cv x1) cscaf) (co (co (cfv (cfv (cv x1) csca) ctopn) (cfv (cv x1) ctopn) ctx) (cfv (cv x1) ctopn) ccn))) (λ x1 . cin ctmd clmod)) ⟶ wceq ctvc (crab (λ x1 . wcel (cfv (cv x1) csca) ctdrg) (λ x1 . ctlm)) ⟶ wceq cust (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . w3a (wss (cv x2) (cpw (cxp (cv x1) (cv x1)))) (wcel (cxp (cv x1) (cv x1)) (cv x2)) (wral (λ x3 . w3a (wral (λ x4 . wss (cv x3) (cv x4) ⟶ wcel (cv x4) (cv x2)) (λ x4 . cpw (cxp (cv x1) (cv x1)))) (wral (λ x4 . wcel (cin (cv x3) (cv x4)) (cv x2)) (λ x4 . cv x2)) (w3a (wss (cres cid (cv x1)) (cv x3)) (wcel (ccnv (cv x3)) (cv x2)) (wrex (λ x4 . wss (ccom (cv x4) (cv x4)) (cv x3)) (λ x4 . cv x2)))) (λ x3 . cv x2))))) ⟶ wceq cutop (cmpt (λ x1 . cuni (crn cust)) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wss (cima (cv x4) (csn (cv x3))) (cv x2)) (λ x4 . cv x1)) (λ x3 . cv x2)) (λ x2 . cpw (cdm (cuni (cv x1)))))) ⟶ wceq cuss (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cv x1) cunif) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs)) crest)) ⟶ wceq cusp (cab (λ x1 . wa (wcel (cfv (cv x1) cuss) (cfv (cfv (cv x1) cbs) cust)) (wceq (cfv (cv x1) ctopn) (cfv (cfv (cv x1) cuss) cutop)))) ⟶ wceq ctus (cmpt (λ x1 . cuni (crn cust)) (λ x1 . co (cpr (cop (cfv cnx cbs) (cdm (cuni (cv x1)))) (cop (cfv cnx cunif) (cv x1))) (cop (cfv cnx cts) (cfv (cv x1) cutop)) csts)) ⟶ wceq cucn (cmpt2 (λ x1 x2 . cuni (crn cust)) (λ x1 x2 . cuni (crn cust)) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wrex (λ x5 . wral (λ x6 . wral (λ x7 . wbr (cv x6) (cv x7) (cv x5) ⟶ wbr (cfv (cv x6) (cv x3)) (cfv (cv x7) (cv x3)) (cv x4)) (λ x7 . cdm (cuni (cv x1)))) (λ x6 . cdm (cuni (cv x1)))) (λ x5 . cv x1)) (λ x4 . cv x2)) (λ x3 . co (cdm (cuni (cv x2))) (cdm (cuni (cv x1))) cmap))) ⟶ wceq ccfilu (cmpt (λ x1 . cuni (crn cust)) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wss (cxp (cv x4) (cv x4)) (cv x3)) (λ x4 . cv x2)) (λ x3 . cv x1)) (λ x2 . cfv (cdm (cuni (cv x1))) cfbas))) ⟶ wceq ccusp (crab (λ x1 . wral (λ x2 . wcel (cv x2) (cfv (cfv (cv x1) cuss) ccfilu) ⟶ wne (co (cfv (cv x1) ctopn) (cv x2) cflim) c0) (λ x2 . cfv (cfv (cv x1) cbs) cfil)) (λ x1 . cusp)) ⟶ wceq cxme (crab (λ x1 . wceq (cfv (cv x1) ctopn) (cfv (cres (cfv (cv x1) cds) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs))) cmopn)) (λ x1 . ctps)) ⟶ wceq cmt (crab (λ x1 . wcel (cres (cfv (cv x1) cds) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs))) (cfv (cfv (cv x1) cbs) cme)) (λ x1 . cxme)) ⟶ wceq ctmt (cmpt (λ x1 . cuni (crn cxmt)) (λ x1 . co (cpr (cop (cfv cnx cbs) (cdm (cdm (cv x1)))) (cop (cfv cnx cds) (cv x1))) (cop (cfv cnx cts) (cfv (cv x1) cmopn)) csts)) ⟶ wceq cnm (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . co (cv x2) (cfv (cv x1) c0g) (cfv (cv x1) cds)))) ⟶ wceq cngp (crab (λ x1 . wss (ccom (cfv (cv x1) cnm) (cfv (cv x1) csg)) (cfv (cv x1) cds)) (λ x1 . cin cgrp cmt)) ⟶ wceq ctng (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cv x1) (cop (cfv cnx cds) (ccom (cv x2) (cfv (cv x1) csg))) csts) (cop (cfv cnx cts) (cfv (ccom (cv x2) (cfv (cv x1) csg)) cmopn)) csts)) ⟶ x0) ⟶ x0
Axiom df_nrg__df_nlm__df_nvc__df_nmo__df_nghm__df_nmhm__df_ii__df_cncf__df_htpy__df_phtpy__df_phtpc__df_pco__df_om1__df_omn__df_pi1__df_pin__df_clm__df_cvs : ∀ x0 : ο . (wceq cnrg (crab (λ x1 . wcel (cfv (cv x1) cnm) (cfv (cv x1) cabv)) (λ x1 . cngp)) ⟶ wceq cnlm (crab (λ x1 . wsbc (λ x2 . wa (wcel (cv x2) cnrg) (wral (λ x3 . wral (λ x4 . wceq (cfv (co (cv x3) (cv x4) (cfv (cv x1) cvsca)) (cfv (cv x1) cnm)) (co (cfv (cv x3) (cfv (cv x2) cnm)) (cfv (cv x4) (cfv (cv x1) cnm)) cmul)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x2) cbs))) (cfv (cv x1) csca)) (λ x1 . cin cngp clmod)) ⟶ wceq cnvc (cin cnlm clvec) ⟶ wceq cnmo (cmpt2 (λ x1 x2 . cngp) (λ x1 x2 . cngp) (λ x1 x2 . cmpt (λ x3 . co (cv x1) (cv x2) cghm) (λ x3 . cinf (crab (λ x4 . wral (λ x5 . wbr (cfv (cfv (cv x5) (cv x3)) (cfv (cv x2) cnm)) (co (cv x4) (cfv (cv x5) (cfv (cv x1) cnm)) cmul) cle) (λ x5 . cfv (cv x1) cbs)) (λ x4 . co cc0 cpnf cico)) cxr clt))) ⟶ wceq cnghm (cmpt2 (λ x1 x2 . cngp) (λ x1 x2 . cngp) (λ x1 x2 . cima (ccnv (co (cv x1) (cv x2) cnmo)) cr)) ⟶ wceq cnmhm (cmpt2 (λ x1 x2 . cnlm) (λ x1 x2 . cnlm) (λ x1 x2 . cin (co (cv x1) (cv x2) clmhm) (co (cv x1) (cv x2) cnghm))) ⟶ wceq cii (cfv (cres (ccom cabs cmin) (cxp (co cc0 c1 cicc) (co cc0 c1 cicc))) cmopn) ⟶ wceq ccncf (cmpt2 (λ x1 x2 . cpw cc) (λ x1 x2 . cpw cc) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wrex (λ x6 . wral (λ x7 . wbr (cfv (co (cv x4) (cv x7) cmin) cabs) (cv x6) clt ⟶ wbr (cfv (co (cfv (cv x4) (cv x3)) (cfv (cv x7) (cv x3)) cmin) cabs) (cv x5) clt) (λ x7 . cv x1)) (λ x6 . crp)) (λ x5 . crp)) (λ x4 . cv x1)) (λ x3 . co (cv x2) (cv x1) cmap))) ⟶ wceq chtpy (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . cmpt2 (λ x3 x4 . co (cv x1) (cv x2) ccn) (λ x3 x4 . co (cv x1) (cv x2) ccn) (λ x3 x4 . crab (λ x5 . wral (λ x6 . wa (wceq (co (cv x6) cc0 (cv x5)) (cfv (cv x6) (cv x3))) (wceq (co (cv x6) c1 (cv x5)) (cfv (cv x6) (cv x4)))) (λ x6 . cuni (cv x1))) (λ x5 . co (co (cv x1) cii ctx) (cv x2) ccn)))) ⟶ wceq cphtpy (cmpt (λ x1 . ctop) (λ x1 . cmpt2 (λ x2 x3 . co cii (cv x1) ccn) (λ x2 x3 . co cii (cv x1) ccn) (λ x2 x3 . crab (λ x4 . wral (λ x5 . wa (wceq (co cc0 (cv x5) (cv x4)) (cfv cc0 (cv x2))) (wceq (co c1 (cv x5) (cv x4)) (cfv c1 (cv x2)))) (λ x5 . co cc0 c1 cicc)) (λ x4 . co (cv x2) (cv x3) (co cii (cv x1) chtpy))))) ⟶ wceq cphtpc (cmpt (λ x1 . ctop) (λ x1 . copab (λ x2 x3 . wa (wss (cpr (cv x2) (cv x3)) (co cii (cv x1) ccn)) (wne (co (cv x2) (cv x3) (cfv (cv x1) cphtpy)) c0)))) ⟶ wceq cpco (cmpt (λ x1 . ctop) (λ x1 . cmpt2 (λ x2 x3 . co cii (cv x1) ccn) (λ x2 x3 . co cii (cv x1) ccn) (λ x2 x3 . cmpt (λ x4 . co cc0 c1 cicc) (λ x4 . cif (wbr (cv x4) (co c1 c2 cdiv) cle) (cfv (co c2 (cv x4) cmul) (cv x2)) (cfv (co (co c2 (cv x4) cmul) c1 cmin) (cv x3)))))) ⟶ wceq comi (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (cv x1)) (λ x1 x2 . ctp (cop (cfv cnx cbs) (crab (λ x3 . wa (wceq (cfv cc0 (cv x3)) (cv x2)) (wceq (cfv c1 (cv x3)) (cv x2))) (λ x3 . co cii (cv x1) ccn))) (cop (cfv cnx cplusg) (cfv (cv x1) cpco)) (cop (cfv cnx cts) (co (cv x1) cii cxko)))) ⟶ wceq comn (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (cv x1)) (λ x1 x2 . cseq (ccom (cmpt2 (λ x3 x4 . cvv) (λ x3 x4 . cvv) (λ x3 x4 . cop (co (cfv (cfv (cv x3) c1st) ctopn) (cfv (cv x3) c2nd) comi) (cxp (co cc0 c1 cicc) (csn (cfv (cv x3) c2nd))))) c1st) (cop (cpr (cop (cfv cnx cbs) (cuni (cv x1))) (cop (cfv cnx cts) (cv x1))) (cv x2)) cc0)) ⟶ wceq cpi1 (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (cv x1)) (λ x1 x2 . co (co (cv x1) (cv x2) comi) (cfv (cv x1) cphtpc) cqus)) ⟶ wceq cpin (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . cuni (cv x1)) (λ x1 x2 . cmpt (λ x3 . cn0) (λ x3 . co (cfv (cfv (cv x3) (co (cv x1) (cv x2) comn)) c1st) (cif (wceq (cv x3) cc0) (copab (λ x4 x5 . wrex (λ x6 . wa (wceq (cfv cc0 (cv x6)) (cv x4)) (wceq (cfv c1 (cv x6)) (cv x5))) (λ x6 . co cii (cv x1) ccn))) (cfv (cfv (cfv (cfv (co (cv x3) c1 cmin) (co (cv x1) (cv x2) comn)) c1st) ctopn) cphtpc)) cqus))) ⟶ wceq cclm (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wa (wceq (cv x2) (co ccnfld (cv x3) cress)) (wcel (cv x3) (cfv ccnfld csubrg))) (cfv (cv x2) cbs)) (cfv (cv x1) csca)) (λ x1 . clmod)) ⟶ wceq ccvs (cin cclm clvec) ⟶ x0) ⟶ x0
Axiom df_cph__df_tch__df_cfil__df_cau__df_cmet__df_cms__df_bn__df_hl__df_rrx__df_ehl__df_ovol__df_vol__df_mbf__df_itg1__df_itg2__df_ibl__df_itg__df_0p : ∀ x0 : ο . (wceq ccph (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . w3a (wceq (cv x2) (co ccnfld (cv x3) cress)) (wss (cima csqrt (cin (cv x3) (co cc0 cpnf cico))) (cv x3)) (wceq (cfv (cv x1) cnm) (cmpt (λ x4 . cfv (cv x1) cbs) (λ x4 . cfv (co (cv x4) (cv x4) (cfv (cv x1) cip)) csqrt)))) (cfv (cv x2) cbs)) (cfv (cv x1) csca)) (λ x1 . cin cphl cnlm)) ⟶ wceq ctch (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . cfv (co (cv x2) (cv x2) (cfv (cv x1) cip)) csqrt)) ctng)) ⟶ wceq ccfil (cmpt (λ x1 . cuni (crn cxmt)) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wss (cima (cv x1) (cxp (cv x4) (cv x4))) (co cc0 (cv x3) cico)) (λ x4 . cv x2)) (λ x3 . crp)) (λ x2 . cfv (cdm (cdm (cv x1))) cfil))) ⟶ wceq cca (cmpt (λ x1 . cuni (crn cxmt)) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wf (cfv (cv x4) cuz) (co (cfv (cv x4) (cv x2)) (cv x3) (cfv (cv x1) cbl)) (cres (cv x2) (cfv (cv x4) cuz))) (λ x4 . cz)) (λ x3 . crp)) (λ x2 . co (cdm (cdm (cv x1))) cc cpm))) ⟶ wceq cms (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wne (co (cfv (cv x2) cmopn) (cv x3) cflim) c0) (λ x3 . cfv (cv x2) ccfil)) (λ x2 . cfv (cv x1) cme))) ⟶ wceq ccms (crab (λ x1 . wsbc (λ x2 . wcel (cres (cfv (cv x1) cds) (cxp (cv x2) (cv x2))) (cfv (cv x2) cms)) (cfv (cv x1) cbs)) (λ x1 . cmt)) ⟶ wceq cbn (crab (λ x1 . wcel (cfv (cv x1) csca) ccms) (λ x1 . cin cnvc ccms)) ⟶ wceq chl (cin cbn ccph) ⟶ wceq crrx (cmpt (λ x1 . cvv) (λ x1 . cfv (co crefld (cv x1) cfrlm) ctch)) ⟶ wceq cehl (cmpt (λ x1 . cn0) (λ x1 . cfv (co c1 (cv x1) cfz) crrx)) ⟶ wceq covol (cmpt (λ x1 . cpw cr) (λ x1 . cinf (crab (λ x2 . wrex (λ x3 . wa (wss (cv x1) (cuni (crn (ccom cioo (cv x3))))) (wceq (cv x2) (csup (crn (cseq caddc (ccom (ccom cabs cmin) (cv x3)) c1)) cxr clt))) (λ x3 . co (cin cle (cxp cr cr)) cn cmap)) (λ x2 . cxr)) cxr clt)) ⟶ wceq cvol (cres covol (cab (λ x1 . wral (λ x2 . wceq (cfv (cv x2) covol) (co (cfv (cin (cv x2) (cv x1)) covol) (cfv (cdif (cv x2) (cv x1)) covol) caddc)) (λ x2 . cima (ccnv covol) cr)))) ⟶ wceq cmbf (crab (λ x1 . wral (λ x2 . wa (wcel (cima (ccnv (ccom cre (cv x1))) (cv x2)) (cdm cvol)) (wcel (cima (ccnv (ccom cim (cv x1))) (cv x2)) (cdm cvol))) (λ x2 . crn cioo)) (λ x1 . co cc cr cpm)) ⟶ wceq citg1 (cmpt (λ x1 . crab (λ x2 . w3a (wf cr cr (cv x2)) (wcel (crn (cv x2)) cfn) (wcel (cfv (cima (ccnv (cv x2)) (cdif cr (csn cc0))) cvol) cr)) (λ x2 . cmbf)) (λ x1 . csu (cdif (crn (cv x1)) (csn cc0)) (λ x2 . co (cv x2) (cfv (cima (ccnv (cv x1)) (csn (cv x2))) cvol) cmul))) ⟶ wceq citg2 (cmpt (λ x1 . co (co cc0 cpnf cicc) cr cmap) (λ x1 . csup (cab (λ x2 . wrex (λ x3 . wa (wbr (cv x3) (cv x1) (cofr cle)) (wceq (cv x2) (cfv (cv x3) citg1))) (λ x3 . cdm citg1))) cxr clt)) ⟶ wceq cibl (crab (λ x1 . wral (λ x2 . wcel (cfv (cmpt (λ x3 . cr) (λ x3 . csb (cfv (co (cfv (cv x3) (cv x1)) (co ci (cv x2) cexp) cdiv) cre) (λ x4 . cif (wa (wcel (cv x3) (cdm (cv x1))) (wbr cc0 (cv x4) cle)) (cv x4) cc0))) citg2) cr) (λ x2 . co cc0 c3 cfz)) (λ x1 . cmbf)) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (citg x1 x2) (csu (co cc0 c3 cfz) (λ x3 . co (co ci (cv x3) cexp) (cfv (cmpt (λ x4 . cr) (λ x4 . csb (cfv (co (x2 x4) (co ci (cv x3) cexp) cdiv) cre) (λ x5 . cif (wa (wcel (cv x4) (x1 x4)) (wbr cc0 (cv x5) cle)) (cv x5) cc0))) citg2) cmul))) ⟶ wceq c0p (cxp cc (csn cc0)) ⟶ x0) ⟶ x0
Axiom df_ditg__df_limc__df_dv__df_dvn__df_cpn__df_mdeg__df_deg1__df_mon1__df_uc1p__df_q1p__df_r1p__df_ig1p__df_ply__df_idp__df_coe__df_dgr__df_quot__df_aa : ∀ x0 : ο . ((∀ x1 x2 x3 : ι → ι → ο . ∀ x4 . wceq (cdit x1 x2 x3) (cif (wbr (x1 x4) (x2 x4) cle) (citg (λ x5 . co (x1 x5) (x2 x5) cioo) x3) (cneg (citg (λ x5 . co (x2 x5) (x1 x5) cioo) x3)))) ⟶ wceq climc (cmpt2 (λ x1 x2 . co cc cc cpm) (λ x1 x2 . cc) (λ x1 x2 . cab (λ x3 . wsbc (λ x4 . wcel (cmpt (λ x5 . cun (cdm (cv x1)) (csn (cv x2))) (λ x5 . cif (wceq (cv x5) (cv x2)) (cv x3) (cfv (cv x5) (cv x1)))) (cfv (cv x2) (co (co (cv x4) (cun (cdm (cv x1)) (csn (cv x2))) crest) (cv x4) ccnp))) (cfv ccnfld ctopn)))) ⟶ wceq cdv (cmpt2 (λ x1 x2 . cpw cc) (λ x1 x2 . co cc (cv x1) cpm) (λ x1 x2 . ciun (λ x3 . cfv (cdm (cv x2)) (cfv (co (cfv ccnfld ctopn) (cv x1) crest) cnt)) (λ x3 . cxp (csn (cv x3)) (co (cmpt (λ x4 . cdif (cdm (cv x2)) (csn (cv x3))) (λ x4 . co (co (cfv (cv x4) (cv x2)) (cfv (cv x3) (cv x2)) cmin) (co (cv x4) (cv x3) cmin) cdiv)) (cv x3) climc)))) ⟶ wceq cdvn (cmpt2 (λ x1 x2 . cpw cc) (λ x1 x2 . co cc (cv x1) cpm) (λ x1 x2 . cseq (ccom (cmpt (λ x3 . cvv) (λ x3 . co (cv x1) (cv x3) cdv)) c1st) (cxp cn0 (csn (cv x2))) cc0)) ⟶ wceq ccpn (cmpt (λ x1 . cpw cc) (λ x1 . cmpt (λ x2 . cn0) (λ x2 . crab (λ x3 . wcel (cfv (cv x2) (co (cv x1) (cv x3) cdvn)) (co (cdm (cv x3)) cc ccncf)) (λ x3 . co cc (cv x1) cpm)))) ⟶ wceq cmdg (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (co (cv x1) (cv x2) cmpl) cbs) (λ x3 . csup (crn (cmpt (λ x4 . co (cv x3) (cfv (cv x2) c0g) csupp) (λ x4 . co ccnfld (cv x4) cgsu))) cxr clt))) ⟶ wceq cdg1 (cmpt (λ x1 . cvv) (λ x1 . co c1o (cv x1) cmdg)) ⟶ wceq cmn1 (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wne (cv x2) (cfv (cfv (cv x1) cpl1) c0g)) (wceq (cfv (cfv (cv x2) (cfv (cv x1) cdg1)) (cfv (cv x2) cco1)) (cfv (cv x1) cur))) (λ x2 . cfv (cfv (cv x1) cpl1) cbs))) ⟶ wceq cuc1p (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wne (cv x2) (cfv (cfv (cv x1) cpl1) c0g)) (wcel (cfv (cfv (cv x2) (cfv (cv x1) cdg1)) (cfv (cv x2) cco1)) (cfv (cv x1) cui))) (λ x2 . cfv (cfv (cv x1) cpl1) cbs))) ⟶ wceq cq1p (cmpt (λ x1 . cvv) (λ x1 . csb (cfv (cv x1) cpl1) (λ x2 . csb (cfv (cv x2) cbs) (λ x3 . cmpt2 (λ x4 x5 . cv x3) (λ x4 x5 . cv x3) (λ x4 x5 . crio (λ x6 . wbr (cfv (co (cv x4) (co (cv x6) (cv x5) (cfv (cv x2) cmulr)) (cfv (cv x2) csg)) (cfv (cv x1) cdg1)) (cfv (cv x5) (cfv (cv x1) cdg1)) clt) (λ x6 . cv x3)))))) ⟶ wceq cr1p (cmpt (λ x1 . cvv) (λ x1 . csb (cfv (cfv (cv x1) cpl1) cbs) (λ x2 . cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . co (cv x3) (co (co (cv x3) (cv x4) (cfv (cv x1) cq1p)) (cv x4) (cfv (cfv (cv x1) cpl1) cmulr)) (cfv (cfv (cv x1) cpl1) csg))))) ⟶ wceq cig1p (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cfv (cv x1) cpl1) clidl) (λ x2 . cif (wceq (cv x2) (csn (cfv (cfv (cv x1) cpl1) c0g))) (cfv (cfv (cv x1) cpl1) c0g) (crio (λ x3 . wceq (cfv (cv x3) (cfv (cv x1) cdg1)) (cinf (cima (cfv (cv x1) cdg1) (cdif (cv x2) (csn (cfv (cfv (cv x1) cpl1) c0g)))) cr clt)) (λ x3 . cin (cv x2) (cfv (cv x1) cmn1)))))) ⟶ wceq cply (cmpt (λ x1 . cpw cc) (λ x1 . cab (λ x2 . wrex (λ x3 . wrex (λ x4 . wceq (cv x2) (cmpt (λ x5 . cc) (λ x5 . csu (co cc0 (cv x3) cfz) (λ x6 . co (cfv (cv x6) (cv x4)) (co (cv x5) (cv x6) cexp) cmul)))) (λ x4 . co (cun (cv x1) (csn cc0)) cn0 cmap)) (λ x3 . cn0)))) ⟶ wceq cidp (cres cid cc) ⟶ wceq ccoe (cmpt (λ x1 . cfv cc cply) (λ x1 . crio (λ x2 . wrex (λ x3 . wa (wceq (cima (cv x2) (cfv (co (cv x3) c1 caddc) cuz)) (csn cc0)) (wceq (cv x1) (cmpt (λ x4 . cc) (λ x4 . csu (co cc0 (cv x3) cfz) (λ x5 . co (cfv (cv x5) (cv x2)) (co (cv x4) (cv x5) cexp) cmul))))) (λ x3 . cn0)) (λ x2 . co cc cn0 cmap))) ⟶ wceq cdgr (cmpt (λ x1 . cfv cc cply) (λ x1 . csup (cima (ccnv (cfv (cv x1) ccoe)) (cdif cc (csn cc0))) cn0 clt)) ⟶ wceq cquot (cmpt2 (λ x1 x2 . cfv cc cply) (λ x1 x2 . cdif (cfv cc cply) (csn c0p)) (λ x1 x2 . crio (λ x3 . wsbc (λ x4 . wo (wceq (cv x4) c0p) (wbr (cfv (cv x4) cdgr) (cfv (cv x2) cdgr) clt)) (co (cv x1) (co (cv x2) (cv x3) (cof cmul)) (cof cmin))) (λ x3 . cfv cc cply))) ⟶ wceq caa (ciun (λ x1 . cdif (cfv cz cply) (csn c0p)) (λ x1 . cima (ccnv (cv x1)) (csn cc0))) ⟶ x0) ⟶ x0
Axiom df_tayl__df_ana__df_ulm__df_log__df_cxp__df_logb__df_asin__df_acos__df_atan__df_area__df_em__df_zeta__df_lgam__df_gam__df_igam__df_cht__df_vma__df_chp : ∀ x0 : ο . (wceq ctayl (cmpt2 (λ x1 x2 . cpr cr cc) (λ x1 x2 . co cc (cv x1) cpm) (λ x1 x2 . cmpt2 (λ x3 x4 . cun cn0 (csn cpnf)) (λ x3 x4 . ciin (λ x5 . cin (co cc0 (cv x3) cicc) cz) (λ x5 . cdm (cfv (cv x5) (co (cv x1) (cv x2) cdvn)))) (λ x3 x4 . ciun (λ x5 . cc) (λ x5 . cxp (csn (cv x5)) (co ccnfld (cmpt (λ x6 . cin (co cc0 (cv x3) cicc) cz) (λ x6 . co (co (cfv (cv x4) (cfv (cv x6) (co (cv x1) (cv x2) cdvn))) (cfv (cv x6) cfa) cdiv) (co (co (cv x5) (cv x4) cmin) (cv x6) cexp) cmul)) ctsu))))) ⟶ wceq cana (cmpt (λ x1 . cpr cr cc) (λ x1 . crab (λ x2 . wral (λ x3 . wcel (cv x3) (cfv (cdm (cin (cv x2) (co cpnf (cv x3) (co (cv x1) (cv x2) ctayl)))) (cfv (co (cfv ccnfld ctopn) (cv x1) crest) cnt))) (λ x3 . cdm (cv x2))) (λ x2 . co cc (cv x1) cpm))) ⟶ wceq culm (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wrex (λ x4 . w3a (wf (cfv (cv x4) cuz) (co cc (cv x1) cmap) (cv x2)) (wf (cv x1) cc (cv x3)) (wral (λ x5 . wrex (λ x6 . wral (λ x7 . wral (λ x8 . wbr (cfv (co (cfv (cv x8) (cfv (cv x7) (cv x2))) (cfv (cv x8) (cv x3)) cmin) cabs) (cv x5) clt) (λ x8 . cv x1)) (λ x7 . cfv (cv x6) cuz)) (λ x6 . cfv (cv x4) cuz)) (λ x5 . crp))) (λ x4 . cz)))) ⟶ wceq clog (ccnv (cres ce (cima (ccnv cim) (co (cneg cpi) cpi cioc)))) ⟶ wceq ccxp (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cc) (λ x1 x2 . cif (wceq (cv x1) cc0) (cif (wceq (cv x2) cc0) c1 cc0) (cfv (co (cv x2) (cfv (cv x1) clog) cmul) ce))) ⟶ wceq clogb (cmpt2 (λ x1 x2 . cdif cc (cpr cc0 c1)) (λ x1 x2 . cdif cc (csn cc0)) (λ x1 x2 . co (cfv (cv x2) clog) (cfv (cv x1) clog) cdiv)) ⟶ wceq casin (cmpt (λ x1 . cc) (λ x1 . co (cneg ci) (cfv (co (co ci (cv x1) cmul) (cfv (co c1 (co (cv x1) c2 cexp) cmin) csqrt) caddc) clog) cmul)) ⟶ wceq cacos (cmpt (λ x1 . cc) (λ x1 . co (co cpi c2 cdiv) (cfv (cv x1) casin) cmin)) ⟶ wceq catan (cmpt (λ x1 . cdif cc (cpr (cneg ci) ci)) (λ x1 . co (co ci c2 cdiv) (co (cfv (co c1 (co ci (cv x1) cmul) cmin) clog) (cfv (co c1 (co ci (cv x1) cmul) caddc) clog) cmin) cmul)) ⟶ wceq carea (cmpt (λ x1 . crab (λ x2 . wa (wral (λ x3 . wcel (cima (cv x2) (csn (cv x3))) (cima (ccnv cvol) cr)) (λ x3 . cr)) (wcel (cmpt (λ x3 . cr) (λ x3 . cfv (cima (cv x2) (csn (cv x3))) cvol)) cibl)) (λ x2 . cpw (cxp cr cr))) (λ x1 . citg (λ x2 . cr) (λ x2 . cfv (cima (cv x1) (csn (cv x2))) cvol))) ⟶ wceq cem (csu cn (λ x1 . co (co c1 (cv x1) cdiv) (cfv (co c1 (co c1 (cv x1) cdiv) caddc) clog) cmin)) ⟶ wceq czeta (crio (λ x1 . wral (λ x2 . wceq (co (co c1 (co c2 (co c1 (cv x2) cmin) ccxp) cmin) (cfv (cv x2) (cv x1)) cmul) (csu cn0 (λ x3 . co (csu (co cc0 (cv x3) cfz) (λ x4 . co (co (co (cneg c1) (cv x4) cexp) (co (cv x3) (cv x4) cbc) cmul) (co (co (cv x4) c1 caddc) (cv x2) ccxp) cmul)) (co c2 (co (cv x3) c1 caddc) cexp) cdiv))) (λ x2 . cdif cc (csn c1))) (λ x1 . co (cdif cc (csn c1)) cc ccncf)) ⟶ wceq clgam (cmpt (λ x1 . cdif cc (cdif cz cn)) (λ x1 . co (csu cn (λ x2 . co (co (cv x1) (cfv (co (co (cv x2) c1 caddc) (cv x2) cdiv) clog) cmul) (cfv (co (co (cv x1) (cv x2) cdiv) c1 caddc) clog) cmin)) (cfv (cv x1) clog) cmin)) ⟶ wceq cgam (ccom ce clgam) ⟶ wceq cigam (cmpt (λ x1 . cc) (λ x1 . cif (wcel (cv x1) (cdif cz cn)) cc0 (co c1 (cfv (cv x1) cgam) cdiv))) ⟶ wceq ccht (cmpt (λ x1 . cr) (λ x1 . csu (cin (co cc0 (cv x1) cicc) cprime) (λ x2 . cfv (cv x2) clog))) ⟶ wceq cvma (cmpt (λ x1 . cn) (λ x1 . csb (crab (λ x2 . wbr (cv x2) (cv x1) cdvds) (λ x2 . cprime)) (λ x2 . cif (wceq (cfv (cv x2) chash) c1) (cfv (cuni (cv x2)) clog) cc0))) ⟶ wceq cchp (cmpt (λ x1 . cr) (λ x1 . csu (co c1 (cfv (cv x1) cfl) cfz) (λ x2 . cfv (cv x2) cvma))) ⟶ x0) ⟶ x0
Axiom df_ppi__df_mu__df_sgm__df_dchr__df_lgs__df_itv__df_lng__df_trkgc__df_trkgb__df_trkgcb__df_trkge__df_trkgld__df_trkg__df_cgrg__df_ismt__df_leg__df_hlg__df_mir : ∀ x0 : ο . (wceq cppi (cmpt (λ x1 . cr) (λ x1 . cfv (cin (co cc0 (cv x1) cicc) cprime) chash)) ⟶ wceq cmu (cmpt (λ x1 . cn) (λ x1 . cif (wrex (λ x2 . wbr (co (cv x2) c2 cexp) (cv x1) cdvds) (λ x2 . cprime)) cc0 (co (cneg c1) (cfv (crab (λ x2 . wbr (cv x2) (cv x1) cdvds) (λ x2 . cprime)) chash) cexp))) ⟶ wceq csgm (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cn) (λ x1 x2 . csu (crab (λ x3 . wbr (cv x3) (cv x2) cdvds) (λ x3 . cn)) (λ x3 . co (cv x3) (cv x1) ccxp))) ⟶ wceq cdchr (cmpt (λ x1 . cn) (λ x1 . csb (cfv (cv x1) czn) (λ x2 . csb (crab (λ x3 . wss (cxp (cdif (cfv (cv x2) cbs) (cfv (cv x2) cui)) (csn cc0)) (cv x3)) (λ x3 . co (cfv (cv x2) cmgp) (cfv ccnfld cmgp) cmhm)) (λ x3 . cpr (cop (cfv cnx cbs) (cv x3)) (cop (cfv cnx cplusg) (cres (cof cmul) (cxp (cv x3) (cv x3)))))))) ⟶ wceq clgs (cmpt2 (λ x1 x2 . cz) (λ x1 x2 . cz) (λ x1 x2 . cif (wceq (cv x2) cc0) (cif (wceq (co (cv x1) c2 cexp) c1) c1 cc0) (co (cif (wa (wbr (cv x2) cc0 clt) (wbr (cv x1) cc0 clt)) (cneg c1) c1) (cfv (cfv (cv x2) cabs) (cseq cmul (cmpt (λ x3 . cn) (λ x3 . cif (wcel (cv x3) cprime) (co (cif (wceq (cv x3) c2) (cif (wbr c2 (cv x1) cdvds) cc0 (cif (wcel (co (cv x1) c8 cmo) (cpr c1 c7)) c1 (cneg c1))) (co (co (co (co (cv x1) (co (co (cv x3) c1 cmin) c2 cdiv) cexp) c1 caddc) (cv x3) cmo) c1 cmin)) (co (cv x3) (cv x2) cpc) cexp) c1)) c1)) cmul))) ⟶ wceq citv (cslot (cdc c1 c6)) ⟶ wceq clng (cslot (cdc c1 c7)) ⟶ wceq cstrkgc (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wa (wral (λ x4 . wral (λ x5 . wceq (co (cv x4) (cv x5) (cv x3)) (co (cv x5) (cv x4) (cv x3))) (λ x5 . cv x2)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wral (λ x6 . wceq (co (cv x4) (cv x5) (cv x3)) (co (cv x6) (cv x6) (cv x3)) ⟶ wceq (cv x4) (cv x5)) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2))) (cfv (cv x1) cds)) (cfv (cv x1) cbs))) ⟶ wceq cstrkgb (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . w3a (wral (λ x4 . wral (λ x5 . wcel (cv x5) (co (cv x4) (cv x4) (cv x3)) ⟶ wceq (cv x4) (cv x5)) (λ x5 . cv x2)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . wa (wcel (cv x7) (co (cv x4) (cv x6) (cv x3))) (wcel (cv x8) (co (cv x5) (cv x6) (cv x3))) ⟶ wrex (λ x9 . wa (wcel (cv x9) (co (cv x7) (cv x5) (cv x3))) (wcel (cv x9) (co (cv x8) (cv x4) (cv x3)))) (λ x9 . cv x2)) (λ x8 . cv x2)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (wral (λ x4 . wral (λ x5 . wrex (λ x6 . wral (λ x7 . wral (λ x8 . wcel (cv x7) (co (cv x6) (cv x8) (cv x3))) (λ x8 . cv x5)) (λ x7 . cv x4)) (λ x6 . cv x2) ⟶ wrex (λ x6 . wral (λ x7 . wral (λ x8 . wcel (cv x6) (co (cv x7) (cv x8) (cv x3))) (λ x8 . cv x5)) (λ x7 . cv x4)) (λ x6 . cv x2)) (λ x5 . cpw (cv x2))) (λ x4 . cpw (cv x2)))) (cfv (cv x1) citv)) (cfv (cv x1) cbs))) ⟶ wceq cstrkgcb (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wa (wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . wral (λ x9 . wral (λ x10 . wral (λ x11 . wral (λ x12 . wa (w3a (wne (cv x5) (cv x6)) (wcel (cv x6) (co (cv x5) (cv x7) (cv x4))) (wcel (cv x10) (co (cv x9) (cv x11) (cv x4)))) (wa (wa (wceq (co (cv x5) (cv x6) (cv x3)) (co (cv x9) (cv x10) (cv x3))) (wceq (co (cv x6) (cv x7) (cv x3)) (co (cv x10) (cv x11) (cv x3)))) (wa (wceq (co (cv x5) (cv x8) (cv x3)) (co (cv x9) (cv x12) (cv x3))) (wceq (co (cv x6) (cv x8) (cv x3)) (co (cv x10) (cv x12) (cv x3))))) ⟶ wceq (co (cv x7) (cv x8) (cv x3)) (co (cv x11) (cv x12) (cv x3))) (λ x12 . cv x2)) (λ x11 . cv x2)) (λ x10 . cv x2)) (λ x9 . cv x2)) (λ x8 . cv x2)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . wrex (λ x9 . wa (wcel (cv x6) (co (cv x5) (cv x9) (cv x4))) (wceq (co (cv x6) (cv x9) (cv x3)) (co (cv x7) (cv x8) (cv x3)))) (λ x9 . cv x2)) (λ x8 . cv x2)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2))) (cfv (cv x1) citv)) (cfv (cv x1) cds)) (cfv (cv x1) cbs))) ⟶ wceq cstrkge (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . w3a (wcel (cv x7) (co (cv x4) (cv x8) (cv x3))) (wcel (cv x7) (co (cv x5) (cv x6) (cv x3))) (wne (cv x4) (cv x7)) ⟶ wrex (λ x9 . wrex (λ x10 . w3a (wcel (cv x5) (co (cv x4) (cv x9) (cv x3))) (wcel (cv x6) (co (cv x4) (cv x10) (cv x3))) (wcel (cv x8) (co (cv x9) (cv x10) (cv x3)))) (λ x10 . cv x2)) (λ x9 . cv x2)) (λ x8 . cv x2)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (λ x4 . cv x2)) (cfv (cv x1) citv)) (cfv (cv x1) cbs))) ⟶ wceq cstrkgld (copab (λ x1 x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wex (λ x6 . wa (wf1 (co c1 (cv x2) cfzo) (cv x3) (cv x6)) (wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . wa (wral (λ x10 . w3a (wceq (co (cfv c1 (cv x6)) (cv x7) (cv x4)) (co (cfv (cv x10) (cv x6)) (cv x7) (cv x4))) (wceq (co (cfv c1 (cv x6)) (cv x8) (cv x4)) (co (cfv (cv x10) (cv x6)) (cv x8) (cv x4))) (wceq (co (cfv c1 (cv x6)) (cv x9) (cv x4)) (co (cfv (cv x10) (cv x6)) (cv x9) (cv x4)))) (λ x10 . co c2 (cv x2) cfzo)) (wn (w3o (wcel (cv x9) (co (cv x7) (cv x8) (cv x5))) (wcel (cv x7) (co (cv x9) (cv x8) (cv x5))) (wcel (cv x8) (co (cv x7) (cv x9) (cv x5)))))) (λ x9 . cv x3)) (λ x8 . cv x3)) (λ x7 . cv x3)))) (cfv (cv x1) citv)) (cfv (cv x1) cds)) (cfv (cv x1) cbs))) ⟶ wceq cstrkg (cin (cin cstrkgc cstrkgb) (cin cstrkgcb (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wceq (cfv (cv x1) clng) (cmpt2 (λ x4 x5 . cv x2) (λ x4 x5 . cdif (cv x2) (csn (cv x4))) (λ x4 x5 . crab (λ x6 . w3o (wcel (cv x6) (co (cv x4) (cv x5) (cv x3))) (wcel (cv x4) (co (cv x6) (cv x5) (cv x3))) (wcel (cv x5) (co (cv x4) (cv x6) (cv x3)))) (λ x6 . cv x2)))) (cfv (cv x1) citv)) (cfv (cv x1) cbs))))) ⟶ wceq ccgrg (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (co (cfv (cv x1) cbs) cr cpm)) (wcel (cv x3) (co (cfv (cv x1) cbs) cr cpm))) (wa (wceq (cdm (cv x2)) (cdm (cv x3))) (wral (λ x4 . wral (λ x5 . wceq (co (cfv (cv x4) (cv x2)) (cfv (cv x5) (cv x2)) (cfv (cv x1) cds)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x1) cds))) (λ x5 . cdm (cv x2))) (λ x4 . cdm (cv x2))))))) ⟶ wceq cismt (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cab (λ x3 . wa (wf1o (cfv (cv x1) cbs) (cfv (cv x2) cbs) (cv x3)) (wral (λ x4 . wral (λ x5 . wceq (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) cds)) (co (cv x4) (cv x5) (cfv (cv x1) cds))) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs))))) ⟶ wceq cleg (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wrex (λ x7 . wrex (λ x8 . wa (wceq (cv x3) (co (cv x7) (cv x8) (cv x5))) (wrex (λ x9 . wa (wcel (cv x9) (co (cv x7) (cv x8) (cv x6))) (wceq (cv x2) (co (cv x7) (cv x9) (cv x5)))) (λ x9 . cv x4))) (λ x8 . cv x4)) (λ x7 . cv x4)) (cfv (cv x1) citv)) (cfv (cv x1) cds)) (cfv (cv x1) cbs)))) ⟶ wceq chlg (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . copab (λ x3 x4 . wa (wa (wcel (cv x3) (cfv (cv x1) cbs)) (wcel (cv x4) (cfv (cv x1) cbs))) (w3a (wne (cv x3) (cv x2)) (wne (cv x4) (cv x2)) (wo (wcel (cv x3) (co (cv x2) (cv x4) (cfv (cv x1) citv))) (wcel (cv x4) (co (cv x2) (cv x3) (cfv (cv x1) citv))))))))) ⟶ wceq cmir (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . cmpt (λ x3 . cfv (cv x1) cbs) (λ x3 . crio (λ x4 . wa (wceq (co (cv x2) (cv x4) (cfv (cv x1) cds)) (co (cv x2) (cv x3) (cfv (cv x1) cds))) (wcel (cv x2) (co (cv x4) (cv x3) (cfv (cv x1) citv)))) (λ x4 . cfv (cv x1) cbs))))) ⟶ x0) ⟶ x0
Axiom df_rag__df_perpg__df_hpg__df_mid__df_lmi__df_cgra__df_inag__df_leag__df_eqlg__df_ttg__df_ee__df_btwn__df_cgr__df_eeng__df_edgf__df_vtx__df_iedg__df_edg : ∀ x0 : ο . (wceq crag (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wceq (cfv (cv x2) chash) c3) (wceq (co (cfv cc0 (cv x2)) (cfv c2 (cv x2)) (cfv (cv x1) cds)) (co (cfv cc0 (cv x2)) (cfv (cfv c2 (cv x2)) (cfv (cfv c1 (cv x2)) (cfv (cv x1) cmir))) (cfv (cv x1) cds)))) (λ x2 . cword (cfv (cv x1) cbs)))) ⟶ wceq cperpg (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (crn (cfv (cv x1) clng))) (wcel (cv x3) (crn (cfv (cv x1) clng)))) (wrex (λ x4 . wral (λ x5 . wral (λ x6 . wcel (cs3 (cv x5) (cv x4) (cv x6)) (cfv (cv x1) crag)) (λ x6 . cv x3)) (λ x5 . cv x2)) (λ x4 . cin (cv x2) (cv x3)))))) ⟶ wceq chpg (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . crn (cfv (cv x1) clng)) (λ x2 . copab (λ x3 x4 . wsbc (λ x5 . wsbc (λ x6 . wrex (λ x7 . wa (wa (wa (wcel (cv x3) (cdif (cv x5) (cv x2))) (wcel (cv x7) (cdif (cv x5) (cv x2)))) (wrex (λ x8 . wcel (cv x8) (co (cv x3) (cv x7) (cv x6))) (λ x8 . cv x2))) (wa (wa (wcel (cv x4) (cdif (cv x5) (cv x2))) (wcel (cv x7) (cdif (cv x5) (cv x2)))) (wrex (λ x8 . wcel (cv x8) (co (cv x4) (cv x7) (cv x6))) (λ x8 . cv x2)))) (λ x7 . cv x5)) (cfv (cv x1) citv)) (cfv (cv x1) cbs))))) ⟶ wceq cmid (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . crio (λ x4 . wceq (cv x3) (cfv (cv x2) (cfv (cv x4) (cfv (cv x1) cmir)))) (λ x4 . cfv (cv x1) cbs)))) ⟶ wceq clmi (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . crn (cfv (cv x1) clng)) (λ x2 . cmpt (λ x3 . cfv (cv x1) cbs) (λ x3 . crio (λ x4 . wa (wcel (co (cv x3) (cv x4) (cfv (cv x1) cmid)) (cv x2)) (wo (wbr (cv x2) (co (cv x3) (cv x4) (cfv (cv x1) clng)) (cfv (cv x1) cperpg)) (wceq (cv x3) (cv x4)))) (λ x4 . cfv (cv x1) cbs))))) ⟶ wceq ccgra (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wsbc (λ x4 . wsbc (λ x5 . wa (wa (wcel (cv x2) (co (cv x4) (co cc0 c3 cfzo) cmap)) (wcel (cv x3) (co (cv x4) (co cc0 c3 cfzo) cmap))) (wrex (λ x6 . wrex (λ x7 . w3a (wbr (cv x2) (cs3 (cv x6) (cfv c1 (cv x3)) (cv x7)) (cfv (cv x1) ccgrg)) (wbr (cv x6) (cfv cc0 (cv x3)) (cfv (cfv c1 (cv x3)) (cv x5))) (wbr (cv x7) (cfv c2 (cv x3)) (cfv (cfv c1 (cv x3)) (cv x5)))) (λ x7 . cv x4)) (λ x6 . cv x4))) (cfv (cv x1) chlg)) (cfv (cv x1) cbs)))) ⟶ wceq cinag (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (cfv (cv x1) cbs)) (wcel (cv x3) (co (cfv (cv x1) cbs) (co cc0 c3 cfzo) cmap))) (wa (w3a (wne (cfv cc0 (cv x3)) (cfv c1 (cv x3))) (wne (cfv c2 (cv x3)) (cfv c1 (cv x3))) (wne (cv x2) (cfv c1 (cv x3)))) (wrex (λ x4 . wa (wcel (cv x4) (co (cfv cc0 (cv x3)) (cfv c2 (cv x3)) (cfv (cv x1) citv))) (wo (wceq (cv x4) (cfv c1 (cv x3))) (wbr (cv x4) (cv x2) (cfv (cfv c1 (cv x3)) (cfv (cv x1) chlg))))) (λ x4 . cfv (cv x1) cbs)))))) ⟶ wceq cleag (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (co (cfv (cv x1) cbs) (co cc0 c3 cfzo) cmap)) (wcel (cv x3) (co (cfv (cv x1) cbs) (co cc0 c3 cfzo) cmap))) (wrex (λ x4 . wa (wbr (cv x4) (cs3 (cfv cc0 (cv x3)) (cfv c1 (cv x3)) (cfv c2 (cv x3))) (cfv (cv x1) cinag)) (wbr (cs3 (cfv cc0 (cv x2)) (cfv c1 (cv x2)) (cfv c2 (cv x2))) (cs3 (cfv cc0 (cv x3)) (cfv c1 (cv x3)) (cv x4)) (cfv (cv x1) ccgra))) (λ x4 . cfv (cv x1) cbs))))) ⟶ wceq ceqlg (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cv x2) (cs3 (cfv c1 (cv x2)) (cfv c2 (cv x2)) (cfv cc0 (cv x2))) (cfv (cv x1) ccgrg)) (λ x2 . co (cfv (cv x1) cbs) (co cc0 c3 cfzo) cmap))) ⟶ wceq cttg (cmpt (λ x1 . cvv) (λ x1 . csb (cmpt2 (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . cfv (cv x1) cbs) (λ x2 x3 . crab (λ x4 . wrex (λ x5 . wceq (co (cv x4) (cv x2) (cfv (cv x1) csg)) (co (cv x5) (co (cv x3) (cv x2) (cfv (cv x1) csg)) (cfv (cv x1) cvsca))) (λ x5 . co cc0 c1 cicc)) (λ x4 . cfv (cv x1) cbs))) (λ x2 . co (co (cv x1) (cop (cfv cnx citv) (cv x2)) csts) (cop (cfv cnx clng) (cmpt2 (λ x3 x4 . cfv (cv x1) cbs) (λ x3 x4 . cfv (cv x1) cbs) (λ x3 x4 . crab (λ x5 . w3o (wcel (cv x5) (co (cv x3) (cv x4) (cv x2))) (wcel (cv x3) (co (cv x5) (cv x4) (cv x2))) (wcel (cv x4) (co (cv x3) (cv x5) (cv x2)))) (λ x5 . cfv (cv x1) cbs)))) csts))) ⟶ wceq cee (cmpt (λ x1 . cn) (λ x1 . co cr (co c1 (cv x1) cfz) cmap)) ⟶ wceq cbtwn (ccnv (coprab (λ x1 x2 x3 . wrex (λ x4 . wa (w3a (wcel (cv x1) (cfv (cv x4) cee)) (wcel (cv x2) (cfv (cv x4) cee)) (wcel (cv x3) (cfv (cv x4) cee))) (wrex (λ x5 . wral (λ x6 . wceq (cfv (cv x6) (cv x3)) (co (co (co c1 (cv x5) cmin) (cfv (cv x6) (cv x1)) cmul) (co (cv x5) (cfv (cv x6) (cv x2)) cmul) caddc)) (λ x6 . co c1 (cv x4) cfz)) (λ x5 . co cc0 c1 cicc))) (λ x4 . cn)))) ⟶ wceq ccgr (copab (λ x1 x2 . wrex (λ x3 . wa (wa (wcel (cv x1) (cxp (cfv (cv x3) cee) (cfv (cv x3) cee))) (wcel (cv x2) (cxp (cfv (cv x3) cee) (cfv (cv x3) cee)))) (wceq (csu (co c1 (cv x3) cfz) (λ x4 . co (co (cfv (cv x4) (cfv (cv x1) c1st)) (cfv (cv x4) (cfv (cv x1) c2nd)) cmin) c2 cexp)) (csu (co c1 (cv x3) cfz) (λ x4 . co (co (cfv (cv x4) (cfv (cv x2) c1st)) (cfv (cv x4) (cfv (cv x2) c2nd)) cmin) c2 cexp)))) (λ x3 . cn))) ⟶ wceq ceeng (cmpt (λ x1 . cn) (λ x1 . cun (cpr (cop (cfv cnx cbs) (cfv (cv x1) cee)) (cop (cfv cnx cds) (cmpt2 (λ x2 x3 . cfv (cv x1) cee) (λ x2 x3 . cfv (cv x1) cee) (λ x2 x3 . csu (co c1 (cv x1) cfz) (λ x4 . co (co (cfv (cv x4) (cv x2)) (cfv (cv x4) (cv x3)) cmin) c2 cexp))))) (cpr (cop (cfv cnx citv) (cmpt2 (λ x2 x3 . cfv (cv x1) cee) (λ x2 x3 . cfv (cv x1) cee) (λ x2 x3 . crab (λ x4 . wbr (cv x4) (cop (cv x2) (cv x3)) cbtwn) (λ x4 . cfv (cv x1) cee)))) (cop (cfv cnx clng) (cmpt2 (λ x2 x3 . cfv (cv x1) cee) (λ x2 x3 . cdif (cfv (cv x1) cee) (csn (cv x2))) (λ x2 x3 . crab (λ x4 . w3o (wbr (cv x4) (cop (cv x2) (cv x3)) cbtwn) (wbr (cv x2) (cop (cv x4) (cv x3)) cbtwn) (wbr (cv x3) (cop (cv x2) (cv x4)) cbtwn)) (λ x4 . cfv (cv x1) cee))))))) ⟶ wceq cedgf (cslot (cdc c1 c8)) ⟶ wceq cvtx (cmpt (λ x1 . cvv) (λ x1 . cif (wcel (cv x1) (cxp cvv cvv)) (cfv (cv x1) c1st) (cfv (cv x1) cbs))) ⟶ wceq ciedg (cmpt (λ x1 . cvv) (λ x1 . cif (wcel (cv x1) (cxp cvv cvv)) (cfv (cv x1) c2nd) (cfv (cv x1) cedgf))) ⟶ wceq cedg (cmpt (λ x1 . cvv) (λ x1 . crn (cfv (cv x1) ciedg))) ⟶ x0) ⟶ x0
Axiom df_uhgr__df_ushgr__df_upgr__df_umgr__df_uspgr__df_usgr__df_subgr__df_fusgr__df_nbgr__df_uvtx__df_cplgr__df_cusgr__df_vtxdg__df_rgr__df_rusgr__df_ewlks__df_wlks__df_wlkson : ∀ x0 : ο . (wceq cuhgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf (cdm (cv x3)) (cdif (cpw (cv x2)) (csn c0)) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq cushgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf1 (cdm (cv x3)) (cdif (cpw (cv x2)) (csn c0)) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq cupgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf (cdm (cv x3)) (crab (λ x4 . wbr (cfv (cv x4) chash) c2 cle) (λ x4 . cdif (cpw (cv x2)) (csn c0))) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq cumgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf (cdm (cv x3)) (crab (λ x4 . wceq (cfv (cv x4) chash) c2) (λ x4 . cdif (cpw (cv x2)) (csn c0))) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq cuspgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf1 (cdm (cv x3)) (crab (λ x4 . wbr (cfv (cv x4) chash) c2 cle) (λ x4 . cdif (cpw (cv x2)) (csn c0))) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq cusgr (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wf1 (cdm (cv x3)) (crab (λ x4 . wceq (cfv (cv x4) chash) c2) (λ x4 . cdif (cpw (cv x2)) (csn c0))) (cv x3)) (cfv (cv x1) ciedg)) (cfv (cv x1) cvtx))) ⟶ wceq csubgr (copab (λ x1 x2 . w3a (wss (cfv (cv x1) cvtx) (cfv (cv x2) cvtx)) (wceq (cfv (cv x1) ciedg) (cres (cfv (cv x2) ciedg) (cdm (cfv (cv x1) ciedg)))) (wss (cfv (cv x1) cedg) (cpw (cfv (cv x1) cvtx))))) ⟶ wceq cfusgr (crab (λ x1 . wcel (cfv (cv x1) cvtx) cfn) (λ x1 . cusgr)) ⟶ wceq cnbgr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cfv (cv x1) cvtx) (λ x1 x2 . crab (λ x3 . wrex (λ x4 . wss (cpr (cv x2) (cv x3)) (cv x4)) (λ x4 . cfv (cv x1) cedg)) (λ x3 . cdif (cfv (cv x1) cvtx) (csn (cv x2))))) ⟶ wceq cuvtx (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wcel (cv x3) (co (cv x1) (cv x2) cnbgr)) (λ x3 . cdif (cfv (cv x1) cvtx) (csn (cv x2)))) (λ x2 . cfv (cv x1) cvtx))) ⟶ wceq ccplgr (cab (λ x1 . wceq (cfv (cv x1) cuvtx) (cfv (cv x1) cvtx))) ⟶ wceq ccusgr (cin cusgr ccplgr) ⟶ wceq cvtxdg (cmpt (λ x1 . cvv) (λ x1 . csb (cfv (cv x1) cvtx) (λ x2 . csb (cfv (cv x1) ciedg) (λ x3 . cmpt (λ x4 . cv x2) (λ x4 . co (cfv (crab (λ x5 . wcel (cv x4) (cfv (cv x5) (cv x3))) (λ x5 . cdm (cv x3))) chash) (cfv (crab (λ x5 . wceq (cfv (cv x5) (cv x3)) (csn (cv x4))) (λ x5 . cdm (cv x3))) chash) cxad))))) ⟶ wceq crgr (copab (λ x1 x2 . wa (wcel (cv x2) cxnn0) (wral (λ x3 . wceq (cfv (cv x3) (cfv (cv x1) cvtxdg)) (cv x2)) (λ x3 . cfv (cv x1) cvtx)))) ⟶ wceq crusgr (copab (λ x1 x2 . wa (wcel (cv x1) cusgr) (wbr (cv x1) (cv x2) crgr))) ⟶ wceq cewlks (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cxnn0) (λ x1 x2 . cab (λ x3 . wsbc (λ x4 . wa (wcel (cv x3) (cword (cdm (cv x4)))) (wral (λ x5 . wbr (cv x2) (cfv (cin (cfv (cfv (co (cv x5) c1 cmin) (cv x3)) (cv x4)) (cfv (cfv (cv x5) (cv x3)) (cv x4))) chash) cle) (λ x5 . co c1 (cfv (cv x3) chash) cfzo))) (cfv (cv x1) ciedg)))) ⟶ wceq cwlks (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . w3a (wcel (cv x2) (cword (cdm (cfv (cv x1) ciedg)))) (wf (co cc0 (cfv (cv x2) chash) cfz) (cfv (cv x1) cvtx) (cv x3)) (wral (λ x4 . wif (wceq (cfv (cv x4) (cv x3)) (cfv (co (cv x4) c1 caddc) (cv x3))) (wceq (cfv (cfv (cv x4) (cv x2)) (cfv (cv x1) ciedg)) (csn (cfv (cv x4) (cv x3)))) (wss (cpr (cfv (cv x4) (cv x3)) (cfv (co (cv x4) c1 caddc) (cv x3))) (cfv (cfv (cv x4) (cv x2)) (cfv (cv x1) ciedg)))) (λ x4 . co cc0 (cfv (cv x2) chash) cfzo))))) ⟶ wceq cwlkson (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . copab (λ x4 x5 . w3a (wbr (cv x4) (cv x5) (cfv (cv x1) cwlks)) (wceq (cfv cc0 (cv x5)) (cv x2)) (wceq (cfv (cfv (cv x4) chash) (cv x5)) (cv x3)))))) ⟶ x0) ⟶ x0
Axiom df_trls__df_trlson__df_pths__df_spths__df_pthson__df_spthson__df_clwlks__df_crcts__df_cycls__df_wwlks__df_wwlksn__df_wwlksnon__df_wspthsn__df_wspthsnon__df_clwwlk__df_clwwlkn__df_clwwlknOLD__df_clwwlknon : ∀ x0 : ο . (wceq ctrls (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) cwlks)) (wfun (ccnv (cv x2)))))) ⟶ wceq ctrlson (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . copab (λ x4 x5 . wa (wbr (cv x4) (cv x5) (co (cv x2) (cv x3) (cfv (cv x1) cwlkson))) (wbr (cv x4) (cv x5) (cfv (cv x1) ctrls)))))) ⟶ wceq cpths (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . w3a (wbr (cv x2) (cv x3) (cfv (cv x1) ctrls)) (wfun (ccnv (cres (cv x3) (co c1 (cfv (cv x2) chash) cfzo)))) (wceq (cin (cima (cv x3) (cpr cc0 (cfv (cv x2) chash))) (cima (cv x3) (co c1 (cfv (cv x2) chash) cfzo))) c0)))) ⟶ wceq cspths (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) ctrls)) (wfun (ccnv (cv x3)))))) ⟶ wceq cpthson (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . copab (λ x4 x5 . wa (wbr (cv x4) (cv x5) (co (cv x2) (cv x3) (cfv (cv x1) ctrlson))) (wbr (cv x4) (cv x5) (cfv (cv x1) cpths)))))) ⟶ wceq cspthson (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . copab (λ x4 x5 . wa (wbr (cv x4) (cv x5) (co (cv x2) (cv x3) (cfv (cv x1) ctrlson))) (wbr (cv x4) (cv x5) (cfv (cv x1) cspths)))))) ⟶ wceq cclwlks (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) cwlks)) (wceq (cfv cc0 (cv x3)) (cfv (cfv (cv x2) chash) (cv x3)))))) ⟶ wceq ccrcts (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) ctrls)) (wceq (cfv cc0 (cv x3)) (cfv (cfv (cv x2) chash) (cv x3)))))) ⟶ wceq ccycls (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) cpths)) (wceq (cfv cc0 (cv x3)) (cfv (cfv (cv x2) chash) (cv x3)))))) ⟶ wceq cwwlks (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wne (cv x2) c0) (wral (λ x3 . wcel (cpr (cfv (cv x3) (cv x2)) (cfv (co (cv x3) c1 caddc) (cv x2))) (cfv (cv x1) cedg)) (λ x3 . co cc0 (co (cfv (cv x2) chash) c1 cmin) cfzo))) (λ x2 . cword (cfv (cv x1) cvtx)))) ⟶ wceq cwwlksn (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wceq (cfv (cv x3) chash) (co (cv x1) c1 caddc)) (λ x3 . cfv (cv x2) cwwlks))) ⟶ wceq cwwlksnon (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . cmpt2 (λ x3 x4 . cfv (cv x2) cvtx) (λ x3 x4 . cfv (cv x2) cvtx) (λ x3 x4 . crab (λ x5 . wa (wceq (cfv cc0 (cv x5)) (cv x3)) (wceq (cfv (cv x1) (cv x5)) (cv x4))) (λ x5 . co (cv x1) (cv x2) cwwlksn)))) ⟶ wceq cwwspthsn (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wex (λ x4 . wbr (cv x4) (cv x3) (cfv (cv x2) cspths))) (λ x3 . co (cv x1) (cv x2) cwwlksn))) ⟶ wceq cwwspthsnon (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . cmpt2 (λ x3 x4 . cfv (cv x2) cvtx) (λ x3 x4 . cfv (cv x2) cvtx) (λ x3 x4 . crab (λ x5 . wex (λ x6 . wbr (cv x6) (cv x5) (co (cv x3) (cv x4) (cfv (cv x2) cspthson)))) (λ x5 . co (cv x3) (cv x4) (co (cv x1) (cv x2) cwwlksnon))))) ⟶ wceq cclwwlk (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . w3a (wne (cv x2) c0) (wral (λ x3 . wcel (cpr (cfv (cv x3) (cv x2)) (cfv (co (cv x3) c1 caddc) (cv x2))) (cfv (cv x1) cedg)) (λ x3 . co cc0 (co (cfv (cv x2) chash) c1 cmin) cfzo)) (wcel (cpr (cfv (cv x2) clsw) (cfv cc0 (cv x2))) (cfv (cv x1) cedg))) (λ x2 . cword (cfv (cv x1) cvtx)))) ⟶ wceq cclwwlkn (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wceq (cfv (cv x3) chash) (cv x1)) (λ x3 . cfv (cv x2) cclwwlk))) ⟶ wceq cclwwlknold (cmpt2 (λ x1 x2 . cn) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wceq (cfv (cv x3) chash) (cv x1)) (λ x3 . cfv (cv x2) cclwwlk))) ⟶ wceq cclwwlknon (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cvtx) (λ x2 x3 . cn0) (λ x2 x3 . crab (λ x4 . wceq (cfv cc0 (cv x4)) (cv x2)) (λ x4 . co (cv x3) (cv x1) cclwwlkn)))) ⟶ x0) ⟶ x0
Axiom df_conngr__df_eupth__df_frgr__df_plig__df_grpo__df_gid__df_ginv__df_gdiv__df_ablo__df_vc__df_nv__df_va__df_ba__df_sm__df_0v__df_vs__df_nmcv__df_ims : ∀ x0 : ο . (wceq cconngr (cab (λ x1 . wsbc (λ x2 . wral (λ x3 . wral (λ x4 . wex (λ x5 . wex (λ x6 . wbr (cv x5) (cv x6) (co (cv x3) (cv x4) (cfv (cv x1) cpthson))))) (λ x4 . cv x2)) (λ x3 . cv x2)) (cfv (cv x1) cvtx))) ⟶ wceq ceupth (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wbr (cv x2) (cv x3) (cfv (cv x1) ctrls)) (wfo (co cc0 (cfv (cv x2) chash) cfzo) (cdm (cfv (cv x1) ciedg)) (cv x2))))) ⟶ wceq cfrgr (cab (λ x1 . wa (wcel (cv x1) cusgr) (wsbc (λ x2 . wsbc (λ x3 . wral (λ x4 . wral (λ x5 . wreu (λ x6 . wss (cpr (cpr (cv x6) (cv x4)) (cpr (cv x6) (cv x5))) (cv x3)) (λ x6 . cv x2)) (λ x5 . cdif (cv x2) (csn (cv x4)))) (λ x4 . cv x2)) (cfv (cv x1) cedg)) (cfv (cv x1) cvtx)))) ⟶ wceq cplig (cab (λ x1 . w3a (wral (λ x2 . wral (λ x3 . wne (cv x2) (cv x3) ⟶ wreu (λ x4 . wa (wcel (cv x2) (cv x4)) (wcel (cv x3) (cv x4))) (λ x4 . cv x1)) (λ x3 . cuni (cv x1))) (λ x2 . cuni (cv x1))) (wral (λ x2 . wrex (λ x3 . wrex (λ x4 . w3a (wne (cv x3) (cv x4)) (wcel (cv x3) (cv x2)) (wcel (cv x4) (cv x2))) (λ x4 . cuni (cv x1))) (λ x3 . cuni (cv x1))) (λ x2 . cv x1)) (wrex (λ x2 . wrex (λ x3 . wrex (λ x4 . wral (λ x5 . wn (w3a (wcel (cv x2) (cv x5)) (wcel (cv x3) (cv x5)) (wcel (cv x4) (cv x5)))) (λ x5 . cv x1)) (λ x4 . cuni (cv x1))) (λ x3 . cuni (cv x1))) (λ x2 . cuni (cv x1))))) ⟶ wceq cgr (cab (λ x1 . wex (λ x2 . w3a (wf (cxp (cv x2) (cv x2)) (cv x2) (cv x1)) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wceq (co (co (cv x3) (cv x4) (cv x1)) (cv x5) (cv x1)) (co (cv x3) (co (cv x4) (cv x5) (cv x1)) (cv x1))) (λ x5 . cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2)) (wrex (λ x3 . wral (λ x4 . wa (wceq (co (cv x3) (cv x4) (cv x1)) (cv x4)) (wrex (λ x5 . wceq (co (cv x5) (cv x4) (cv x1)) (cv x3)) (λ x5 . cv x2))) (λ x4 . cv x2)) (λ x3 . cv x2))))) ⟶ wceq cgi (cmpt (λ x1 . cvv) (λ x1 . crio (λ x2 . wral (λ x3 . wa (wceq (co (cv x2) (cv x3) (cv x1)) (cv x3)) (wceq (co (cv x3) (cv x2) (cv x1)) (cv x3))) (λ x3 . crn (cv x1))) (λ x2 . crn (cv x1)))) ⟶ wceq cgn (cmpt (λ x1 . cgr) (λ x1 . cmpt (λ x2 . crn (cv x1)) (λ x2 . crio (λ x3 . wceq (co (cv x3) (cv x2) (cv x1)) (cfv (cv x1) cgi)) (λ x3 . crn (cv x1))))) ⟶ wceq cgs (cmpt (λ x1 . cgr) (λ x1 . cmpt2 (λ x2 x3 . crn (cv x1)) (λ x2 x3 . crn (cv x1)) (λ x2 x3 . co (cv x2) (cfv (cv x3) (cfv (cv x1) cgn)) (cv x1)))) ⟶ wceq cablo (crab (λ x1 . wral (λ x2 . wral (λ x3 . wceq (co (cv x2) (cv x3) (cv x1)) (co (cv x3) (cv x2) (cv x1))) (λ x3 . crn (cv x1))) (λ x2 . crn (cv x1))) (λ x1 . cgr)) ⟶ wceq cvc (copab (λ x1 x2 . w3a (wcel (cv x1) cablo) (wf (cxp cc (crn (cv x1))) (crn (cv x1)) (cv x2)) (wral (λ x3 . wa (wceq (co c1 (cv x3) (cv x2)) (cv x3)) (wral (λ x4 . wa (wral (λ x5 . wceq (co (cv x4) (co (cv x3) (cv x5) (cv x1)) (cv x2)) (co (co (cv x4) (cv x3) (cv x2)) (co (cv x4) (cv x5) (cv x2)) (cv x1))) (λ x5 . crn (cv x1))) (wral (λ x5 . wa (wceq (co (co (cv x4) (cv x5) caddc) (cv x3) (cv x2)) (co (co (cv x4) (cv x3) (cv x2)) (co (cv x5) (cv x3) (cv x2)) (cv x1))) (wceq (co (co (cv x4) (cv x5) cmul) (cv x3) (cv x2)) (co (cv x4) (co (cv x5) (cv x3) (cv x2)) (cv x2)))) (λ x5 . cc))) (λ x4 . cc))) (λ x3 . crn (cv x1))))) ⟶ wceq cnv (coprab (λ x1 x2 x3 . w3a (wcel (cop (cv x1) (cv x2)) cvc) (wf (crn (cv x1)) cr (cv x3)) (wral (λ x4 . w3a (wceq (cfv (cv x4) (cv x3)) cc0 ⟶ wceq (cv x4) (cfv (cv x1) cgi)) (wral (λ x5 . wceq (cfv (co (cv x5) (cv x4) (cv x2)) (cv x3)) (co (cfv (cv x5) cabs) (cfv (cv x4) (cv x3)) cmul)) (λ x5 . cc)) (wral (λ x5 . wbr (cfv (co (cv x4) (cv x5) (cv x1)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) caddc) cle) (λ x5 . crn (cv x1)))) (λ x4 . crn (cv x1))))) ⟶ wceq cpv (ccom c1st c1st) ⟶ wceq cba (cmpt (λ x1 . cvv) (λ x1 . crn (cfv (cv x1) cpv))) ⟶ wceq cns (ccom c2nd c1st) ⟶ wceq cn0v (ccom cgi cpv) ⟶ wceq cnsb (ccom cgs cpv) ⟶ wceq cnmcv c2nd ⟶ wceq cims (cmpt (λ x1 . cnv) (λ x1 . ccom (cfv (cv x1) cnmcv) (cfv (cv x1) cnsb))) ⟶ x0) ⟶ x0
Axiom df_dip__df_ssp__df_lno__df_nmoo__df_blo__df_0o__df_aj__df_hmo__df_ph__df_cbn__df_hlo__df_hnorm__df_hba__df_h0v__df_hvsub__df_hlim__df_hcau__ax_hilex : ∀ x0 : ο . (wceq cdip (cmpt (λ x1 . cnv) (λ x1 . cmpt2 (λ x2 x3 . cfv (cv x1) cba) (λ x2 x3 . cfv (cv x1) cba) (λ x2 x3 . co (csu (co c1 c4 cfz) (λ x4 . co (co ci (cv x4) cexp) (co (cfv (co (cv x2) (co (co ci (cv x4) cexp) (cv x3) (cfv (cv x1) cns)) (cfv (cv x1) cpv)) (cfv (cv x1) cnmcv)) c2 cexp) cmul)) c4 cdiv))) ⟶ wceq css (cmpt (λ x1 . cnv) (λ x1 . crab (λ x2 . w3a (wss (cfv (cv x2) cpv) (cfv (cv x1) cpv)) (wss (cfv (cv x2) cns) (cfv (cv x1) cns)) (wss (cfv (cv x2) cnmcv) (cfv (cv x1) cnmcv))) (λ x2 . cnv))) ⟶ wceq clno (cmpt2 (λ x1 x2 . cnv) (λ x1 x2 . cnv) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wceq (cfv (co (co (cv x4) (cv x5) (cfv (cv x1) cns)) (cv x6) (cfv (cv x1) cpv)) (cv x3)) (co (co (cv x4) (cfv (cv x5) (cv x3)) (cfv (cv x2) cns)) (cfv (cv x6) (cv x3)) (cfv (cv x2) cpv))) (λ x6 . cfv (cv x1) cba)) (λ x5 . cfv (cv x1) cba)) (λ x4 . cc)) (λ x3 . co (cfv (cv x2) cba) (cfv (cv x1) cba) cmap))) ⟶ wceq cnmoo (cmpt2 (λ x1 x2 . cnv) (λ x1 x2 . cnv) (λ x1 x2 . cmpt (λ x3 . co (cfv (cv x2) cba) (cfv (cv x1) cba) cmap) (λ x3 . csup (cab (λ x4 . wrex (λ x5 . wa (wbr (cfv (cv x5) (cfv (cv x1) cnmcv)) c1 cle) (wceq (cv x4) (cfv (cfv (cv x5) (cv x3)) (cfv (cv x2) cnmcv)))) (λ x5 . cfv (cv x1) cba))) cxr clt))) ⟶ wceq cblo (cmpt2 (λ x1 x2 . cnv) (λ x1 x2 . cnv) (λ x1 x2 . crab (λ x3 . wbr (cfv (cv x3) (co (cv x1) (cv x2) cnmoo)) cpnf clt) (λ x3 . co (cv x1) (cv x2) clno))) ⟶ wceq c0o (cmpt2 (λ x1 x2 . cnv) (λ x1 x2 . cnv) (λ x1 x2 . cxp (cfv (cv x1) cba) (csn (cfv (cv x2) cn0v)))) ⟶ wceq caj (cmpt2 (λ x1 x2 . cnv) (λ x1 x2 . cnv) (λ x1 x2 . copab (λ x3 x4 . w3a (wf (cfv (cv x1) cba) (cfv (cv x2) cba) (cv x3)) (wf (cfv (cv x2) cba) (cfv (cv x1) cba) (cv x4)) (wral (λ x5 . wral (λ x6 . wceq (co (cfv (cv x5) (cv x3)) (cv x6) (cfv (cv x2) cdip)) (co (cv x5) (cfv (cv x6) (cv x4)) (cfv (cv x1) cdip))) (λ x6 . cfv (cv x2) cba)) (λ x5 . cfv (cv x1) cba))))) ⟶ wceq chmo (cmpt (λ x1 . cnv) (λ x1 . crab (λ x2 . wceq (cfv (cv x2) (co (cv x1) (cv x1) caj)) (cv x2)) (λ x2 . cdm (co (cv x1) (cv x1) caj)))) ⟶ wceq ccphlo (cin cnv (coprab (λ x1 x2 x3 . wral (λ x4 . wral (λ x5 . wceq (co (co (cfv (co (cv x4) (cv x5) (cv x1)) (cv x3)) c2 cexp) (co (cfv (co (cv x4) (co (cneg c1) (cv x5) (cv x2)) (cv x1)) (cv x3)) c2 cexp) caddc) (co c2 (co (co (cfv (cv x4) (cv x3)) c2 cexp) (co (cfv (cv x5) (cv x3)) c2 cexp) caddc) cmul)) (λ x5 . crn (cv x1))) (λ x4 . crn (cv x1))))) ⟶ wceq ccbn (crab (λ x1 . wcel (cfv (cv x1) cims) (cfv (cfv (cv x1) cba) cms)) (λ x1 . cnv)) ⟶ wceq chlo (cin ccbn ccphlo) ⟶ wceq cno (cmpt (λ x1 . cdm (cdm csp)) (λ x1 . cfv (co (cv x1) (cv x1) csp) csqrt)) ⟶ wceq chil (cfv (cop (cop cva csm) cno) cba) ⟶ wceq c0v (cfv (cop (cop cva csm) cno) cn0v) ⟶ wceq cmv (cmpt2 (λ x1 x2 . chil) (λ x1 x2 . chil) (λ x1 x2 . co (cv x1) (co (cneg c1) (cv x2) csm) cva)) ⟶ wceq chli (copab (λ x1 x2 . wa (wa (wf cn chil (cv x1)) (wcel (cv x2) chil)) (wral (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cfv (co (cfv (cv x5) (cv x1)) (cv x2) cmv) cno) (cv x3) clt) (λ x5 . cfv (cv x4) cuz)) (λ x4 . cn)) (λ x3 . crp)))) ⟶ wceq ccau (crab (λ x1 . wral (λ x2 . wrex (λ x3 . wral (λ x4 . wbr (cfv (co (cfv (cv x3) (cv x1)) (cfv (cv x4) (cv x1)) cmv) cno) (cv x2) clt) (λ x4 . cfv (cv x3) cuz)) (λ x3 . cn)) (λ x2 . crp)) (λ x1 . co chil cn cmap)) ⟶ wcel chil cvv ⟶ x0) ⟶ x0
Axiom ax_hfvadd__ax_hvcom__ax_hvass__ax_hv0cl__ax_hvaddid__ax_hfvmul__ax_hvmulid__ax_hvmulass__ax_hvdistr1__ax_hvdistr2__ax_hvmul0__ax_hfi__ax_his1__ax_his2__ax_his3__ax_his4__ax_hcompl__df_sh : ∀ x0 : ο . (wf (cxp chil chil) chil cva ⟶ (∀ x1 x2 : ι → ο . wa (wcel x1 chil) (wcel x2 chil) ⟶ wceq (co x1 x2 cva) (co x2 x1 cva)) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 chil) (wcel x2 chil) (wcel x3 chil) ⟶ wceq (co (co x1 x2 cva) x3 cva) (co x1 (co x2 x3 cva) cva)) ⟶ wcel c0v chil ⟶ (∀ x1 : ι → ο . wcel x1 chil ⟶ wceq (co x1 c0v cva) x1) ⟶ wf (cxp cc chil) chil csm ⟶ (∀ x1 : ι → ο . wcel x1 chil ⟶ wceq (co c1 x1 csm) x1) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 cc) (wcel x2 cc) (wcel x3 chil) ⟶ wceq (co (co x1 x2 cmul) x3 csm) (co x1 (co x2 x3 csm) csm)) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 cc) (wcel x2 chil) (wcel x3 chil) ⟶ wceq (co x1 (co x2 x3 cva) csm) (co (co x1 x2 csm) (co x1 x3 csm) cva)) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 cc) (wcel x2 cc) (wcel x3 chil) ⟶ wceq (co (co x1 x2 caddc) x3 csm) (co (co x1 x3 csm) (co x2 x3 csm) cva)) ⟶ (∀ x1 : ι → ο . wcel x1 chil ⟶ wceq (co cc0 x1 csm) c0v) ⟶ wf (cxp chil chil) cc csp ⟶ (∀ x1 x2 : ι → ο . wa (wcel x1 chil) (wcel x2 chil) ⟶ wceq (co x1 x2 csp) (cfv (co x2 x1 csp) ccj)) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 chil) (wcel x2 chil) (wcel x3 chil) ⟶ wceq (co (co x1 x2 cva) x3 csp) (co (co x1 x3 csp) (co x2 x3 csp) caddc)) ⟶ (∀ x1 x2 x3 : ι → ο . w3a (wcel x1 cc) (wcel x2 chil) (wcel x3 chil) ⟶ wceq (co (co x1 x2 csm) x3 csp) (co x1 (co x2 x3 csp) cmul)) ⟶ (∀ x1 : ι → ο . wa (wcel x1 chil) (wne x1 c0v) ⟶ wbr cc0 (co x1 x1 csp) clt) ⟶ (∀ x1 : ι → ο . wcel x1 ccau ⟶ wrex (λ x2 . wbr x1 (cv x2) chli) (λ x2 . chil)) ⟶ wceq csh (crab (λ x1 . w3a (wcel c0v (cv x1)) (wss (cima cva (cxp (cv x1) (cv x1))) (cv x1)) (wss (cima csm (cxp cc (cv x1))) (cv x1))) (λ x1 . cpw chil)) ⟶ x0) ⟶ x0
Axiom df_ch__df_oc__df_ch0__df_shs__df_span__df_chj__df_chsup__df_pjh__df_cm__df_hosum__df_homul__df_hodif__df_hfsum__df_hfmul__df_h0op__df_iop__df_nmop__df_cnop : ∀ x0 : ο . (wceq cch (crab (λ x1 . wss (cima chli (co (cv x1) cn cmap)) (cv x1)) (λ x1 . csh)) ⟶ wceq cort (cmpt (λ x1 . cpw chil) (λ x1 . crab (λ x2 . wral (λ x3 . wceq (co (cv x2) (cv x3) csp) cc0) (λ x3 . cv x1)) (λ x2 . chil))) ⟶ wceq c0h (csn c0v) ⟶ wceq cph (cmpt2 (λ x1 x2 . csh) (λ x1 x2 . csh) (λ x1 x2 . cima cva (cxp (cv x1) (cv x2)))) ⟶ wceq cspn (cmpt (λ x1 . cpw chil) (λ x1 . cint (crab (λ x2 . wss (cv x1) (cv x2)) (λ x2 . csh)))) ⟶ wceq chj (cmpt2 (λ x1 x2 . cpw chil) (λ x1 x2 . cpw chil) (λ x1 x2 . cfv (cfv (cun (cv x1) (cv x2)) cort) cort)) ⟶ wceq chsup (cmpt (λ x1 . cpw (cpw chil)) (λ x1 . cfv (cfv (cuni (cv x1)) cort) cort)) ⟶ wceq cpjh (cmpt (λ x1 . cch) (λ x1 . cmpt (λ x2 . chil) (λ x2 . crio (λ x3 . wrex (λ x4 . wceq (cv x2) (co (cv x3) (cv x4) cva)) (λ x4 . cfv (cv x1) cort)) (λ x3 . cv x1)))) ⟶ wceq ccm (copab (λ x1 x2 . wa (wa (wcel (cv x1) cch) (wcel (cv x2) cch)) (wceq (cv x1) (co (cin (cv x1) (cv x2)) (cin (cv x1) (cfv (cv x2) cort)) chj)))) ⟶ wceq chos (cmpt2 (λ x1 x2 . co chil chil cmap) (λ x1 x2 . co chil chil cmap) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) cva))) ⟶ wceq chot (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . co chil chil cmap) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (cv x1) (cfv (cv x3) (cv x2)) csm))) ⟶ wceq chod (cmpt2 (λ x1 x2 . co chil chil cmap) (λ x1 x2 . co chil chil cmap) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) cmv))) ⟶ wceq chfs (cmpt2 (λ x1 x2 . co cc chil cmap) (λ x1 x2 . co cc chil cmap) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) caddc))) ⟶ wceq chft (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . co cc chil cmap) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (cv x1) (cfv (cv x3) (cv x2)) cmul))) ⟶ wceq ch0o (cfv c0h cpjh) ⟶ wceq chio (cfv chil cpjh) ⟶ wceq cnop (cmpt (λ x1 . co chil chil cmap) (λ x1 . csup (cab (λ x2 . wrex (λ x3 . wa (wbr (cfv (cv x3) cno) c1 cle) (wceq (cv x2) (cfv (cfv (cv x3) (cv x1)) cno))) (λ x3 . chil))) cxr clt)) ⟶ wceq ccop (crab (λ x1 . wral (λ x2 . wral (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cfv (co (cv x5) (cv x2) cmv) cno) (cv x4) clt ⟶ wbr (cfv (co (cfv (cv x5) (cv x1)) (cfv (cv x2) (cv x1)) cmv) cno) (cv x3) clt) (λ x5 . chil)) (λ x4 . crp)) (λ x3 . crp)) (λ x2 . chil)) (λ x1 . co chil chil cmap)) ⟶ x0) ⟶ x0
Axiom df_lnop__df_bdop__df_unop__df_hmop__df_nmfn__df_nlfn__df_cnfn__df_lnfn__df_adjh__df_bra__df_kb__df_leop__df_eigvec__df_eigval__df_spec__df_st__df_hst__df_cv : ∀ x0 : ο . (wceq clo (crab (λ x1 . wral (λ x2 . wral (λ x3 . wral (λ x4 . wceq (cfv (co (co (cv x2) (cv x3) csm) (cv x4) cva) (cv x1)) (co (co (cv x2) (cfv (cv x3) (cv x1)) csm) (cfv (cv x4) (cv x1)) cva)) (λ x4 . chil)) (λ x3 . chil)) (λ x2 . cc)) (λ x1 . co chil chil cmap)) ⟶ wceq cbo (crab (λ x1 . wbr (cfv (cv x1) cnop) cpnf clt) (λ x1 . clo)) ⟶ wceq cuo (cab (λ x1 . wa (wfo chil chil (cv x1)) (wral (λ x2 . wral (λ x3 . wceq (co (cfv (cv x2) (cv x1)) (cfv (cv x3) (cv x1)) csp) (co (cv x2) (cv x3) csp)) (λ x3 . chil)) (λ x2 . chil)))) ⟶ wceq cho (crab (λ x1 . wral (λ x2 . wral (λ x3 . wceq (co (cv x2) (cfv (cv x3) (cv x1)) csp) (co (cfv (cv x2) (cv x1)) (cv x3) csp)) (λ x3 . chil)) (λ x2 . chil)) (λ x1 . co chil chil cmap)) ⟶ wceq cnmf (cmpt (λ x1 . co cc chil cmap) (λ x1 . csup (cab (λ x2 . wrex (λ x3 . wa (wbr (cfv (cv x3) cno) c1 cle) (wceq (cv x2) (cfv (cfv (cv x3) (cv x1)) cabs))) (λ x3 . chil))) cxr clt)) ⟶ wceq cnl (cmpt (λ x1 . co cc chil cmap) (λ x1 . cima (ccnv (cv x1)) (csn cc0))) ⟶ wceq ccnfn (crab (λ x1 . wral (λ x2 . wral (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cfv (co (cv x5) (cv x2) cmv) cno) (cv x4) clt ⟶ wbr (cfv (co (cfv (cv x5) (cv x1)) (cfv (cv x2) (cv x1)) cmin) cabs) (cv x3) clt) (λ x5 . chil)) (λ x4 . crp)) (λ x3 . crp)) (λ x2 . chil)) (λ x1 . co cc chil cmap)) ⟶ wceq clf (crab (λ x1 . wral (λ x2 . wral (λ x3 . wral (λ x4 . wceq (cfv (co (co (cv x2) (cv x3) csm) (cv x4) cva) (cv x1)) (co (co (cv x2) (cfv (cv x3) (cv x1)) cmul) (cfv (cv x4) (cv x1)) caddc)) (λ x4 . chil)) (λ x3 . chil)) (λ x2 . cc)) (λ x1 . co cc chil cmap)) ⟶ wceq cado (copab (λ x1 x2 . w3a (wf chil chil (cv x1)) (wf chil chil (cv x2)) (wral (λ x3 . wral (λ x4 . wceq (co (cfv (cv x3) (cv x1)) (cv x4) csp) (co (cv x3) (cfv (cv x4) (cv x2)) csp)) (λ x4 . chil)) (λ x3 . chil)))) ⟶ wceq cbr (cmpt (λ x1 . chil) (λ x1 . cmpt (λ x2 . chil) (λ x2 . co (cv x2) (cv x1) csp))) ⟶ wceq ck (cmpt2 (λ x1 x2 . chil) (λ x1 x2 . chil) (λ x1 x2 . cmpt (λ x3 . chil) (λ x3 . co (co (cv x3) (cv x2) csp) (cv x1) csm))) ⟶ wceq cleo (copab (λ x1 x2 . wa (wcel (co (cv x2) (cv x1) chod) cho) (wral (λ x3 . wbr cc0 (co (cfv (cv x3) (co (cv x2) (cv x1) chod)) (cv x3) csp) cle) (λ x3 . chil)))) ⟶ wceq cei (cmpt (λ x1 . co chil chil cmap) (λ x1 . crab (λ x2 . wrex (λ x3 . wceq (cfv (cv x2) (cv x1)) (co (cv x3) (cv x2) csm)) (λ x3 . cc)) (λ x2 . cdif chil c0h))) ⟶ wceq cel (cmpt (λ x1 . co chil chil cmap) (λ x1 . cmpt (λ x2 . cfv (cv x1) cei) (λ x2 . co (co (cfv (cv x2) (cv x1)) (cv x2) csp) (co (cfv (cv x2) cno) c2 cexp) cdiv))) ⟶ wceq cspc (cmpt (λ x1 . co chil chil cmap) (λ x1 . crab (λ x2 . wn (wf1 chil chil (co (cv x1) (co (cv x2) (cres cid chil) chot) chod))) (λ x2 . cc))) ⟶ wceq cst (crab (λ x1 . wa (wceq (cfv chil (cv x1)) c1) (wral (λ x2 . wral (λ x3 . wss (cv x2) (cfv (cv x3) cort) ⟶ wceq (cfv (co (cv x2) (cv x3) chj) (cv x1)) (co (cfv (cv x2) (cv x1)) (cfv (cv x3) (cv x1)) caddc)) (λ x3 . cch)) (λ x2 . cch))) (λ x1 . co (co cc0 c1 cicc) cch cmap)) ⟶ wceq chst (crab (λ x1 . wa (wceq (cfv (cfv chil (cv x1)) cno) c1) (wral (λ x2 . wral (λ x3 . wss (cv x2) (cfv (cv x3) cort) ⟶ wa (wceq (co (cfv (cv x2) (cv x1)) (cfv (cv x3) (cv x1)) csp) cc0) (wceq (cfv (co (cv x2) (cv x3) chj) (cv x1)) (co (cfv (cv x2) (cv x1)) (cfv (cv x3) (cv x1)) cva))) (λ x3 . cch)) (λ x2 . cch))) (λ x1 . co chil cch cmap)) ⟶ wceq ccv (copab (λ x1 x2 . wa (wa (wcel (cv x1) cch) (wcel (cv x2) cch)) (wa (wpss (cv x1) (cv x2)) (wn (wrex (λ x3 . wa (wpss (cv x1) (cv x3)) (wpss (cv x3) (cv x2))) (λ x3 . cch)))))) ⟶ x0) ⟶ x0
Axiom df_md__df_dmd__df_at__df_dp2__df_dp__df_xdiv__ax_xrssca__ax_xrsvsca__df_omnd__df_ogrp__df_sgns__df_inftm__df_archi__df_slmd__df_orng__df_ofld__df_resv__df_smat : ∀ x0 : ο . (wceq cmd (copab (λ x1 x2 . wa (wa (wcel (cv x1) cch) (wcel (cv x2) cch)) (wral (λ x3 . wss (cv x3) (cv x2) ⟶ wceq (cin (co (cv x3) (cv x1) chj) (cv x2)) (co (cv x3) (cin (cv x1) (cv x2)) chj)) (λ x3 . cch)))) ⟶ wceq cdmd (copab (λ x1 x2 . wa (wa (wcel (cv x1) cch) (wcel (cv x2) cch)) (wral (λ x3 . wss (cv x2) (cv x3) ⟶ wceq (co (cin (cv x3) (cv x1)) (cv x2) chj) (cin (cv x3) (co (cv x1) (cv x2) chj))) (λ x3 . cch)))) ⟶ wceq cat (crab (λ x1 . wbr c0h (cv x1) ccv) (λ x1 . cch)) ⟶ (∀ x1 x2 : ι → ο . wceq (cdp2 x1 x2) (co x1 (co x2 (cdc c1 cc0) cdiv) caddc)) ⟶ wceq cdp (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . cr) (λ x1 x2 . cdp2 (cv x1) (cv x2))) ⟶ wceq cxdiv (cmpt2 (λ x1 x2 . cxr) (λ x1 x2 . cdif cr (csn cc0)) (λ x1 x2 . crio (λ x3 . wceq (co (cv x2) (cv x3) cxmu) (cv x1)) (λ x3 . cxr))) ⟶ wceq crefld (cfv cxrs csca) ⟶ wceq cxmu (cfv cxrs cvsca) ⟶ wceq comnd (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wa (wcel (cv x1) ctos) (wral (λ x5 . wral (λ x6 . wral (λ x7 . wbr (cv x5) (cv x6) (cv x4) ⟶ wbr (co (cv x5) (cv x7) (cv x3)) (co (cv x6) (cv x7) (cv x3)) (cv x4)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2))) (cfv (cv x1) cple)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x1 . cmnd)) ⟶ wceq cogrp (cin cgrp comnd) ⟶ wceq csgns (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . cif (wceq (cv x2) (cfv (cv x1) c0g)) cc0 (cif (wbr (cfv (cv x1) c0g) (cv x2) (cfv (cv x1) cplt)) c1 (cneg c1))))) ⟶ wceq cinftm (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (cfv (cv x1) cbs)) (wcel (cv x3) (cfv (cv x1) cbs))) (wa (wbr (cfv (cv x1) c0g) (cv x2) (cfv (cv x1) cplt)) (wral (λ x4 . wbr (co (cv x4) (cv x2) (cfv (cv x1) cmg)) (cv x3) (cfv (cv x1) cplt)) (λ x4 . cn)))))) ⟶ wceq carchi (cab (λ x1 . wceq (cfv (cv x1) cinftm) c0)) ⟶ wceq cslmd (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wsbc (λ x7 . wsbc (λ x8 . wa (wcel (cv x5) csrg) (wral (λ x9 . wral (λ x10 . wral (λ x11 . wral (λ x12 . wa (w3a (wcel (co (cv x10) (cv x12) (cv x4)) (cv x2)) (wceq (co (cv x10) (co (cv x12) (cv x11) (cv x3)) (cv x4)) (co (co (cv x10) (cv x12) (cv x4)) (co (cv x10) (cv x11) (cv x4)) (cv x3))) (wceq (co (co (cv x9) (cv x10) (cv x7)) (cv x12) (cv x4)) (co (co (cv x9) (cv x12) (cv x4)) (co (cv x10) (cv x12) (cv x4)) (cv x3)))) (w3a (wceq (co (co (cv x9) (cv x10) (cv x8)) (cv x12) (cv x4)) (co (cv x9) (co (cv x10) (cv x12) (cv x4)) (cv x4))) (wceq (co (cfv (cv x5) cur) (cv x12) (cv x4)) (cv x12)) (wceq (co (cfv (cv x5) c0g) (cv x12) (cv x4)) (cfv (cv x1) c0g)))) (λ x12 . cv x2)) (λ x11 . cv x2)) (λ x10 . cv x6)) (λ x9 . cv x6))) (cfv (cv x5) cmulr)) (cfv (cv x5) cplusg)) (cfv (cv x5) cbs)) (cfv (cv x1) csca)) (cfv (cv x1) cvsca)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs)) (λ x1 . ccmn)) ⟶ wceq corng (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wral (λ x6 . wral (λ x7 . wa (wbr (cv x3) (cv x6) (cv x5)) (wbr (cv x3) (cv x7) (cv x5)) ⟶ wbr (cv x3) (co (cv x6) (cv x7) (cv x4)) (cv x5)) (λ x7 . cv x2)) (λ x6 . cv x2)) (cfv (cv x1) cple)) (cfv (cv x1) cmulr)) (cfv (cv x1) c0g)) (cfv (cv x1) cbs)) (λ x1 . cin crg cogrp)) ⟶ wceq cofld (cin cfield corng) ⟶ wceq cresv (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cif (wss (cfv (cfv (cv x1) csca) cbs) (cv x2)) (cv x1) (co (cv x1) (cop (cfv cnx csca) (co (cfv (cv x1) csca) (cv x2) cress)) csts))) ⟶ wceq csmat (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cn) (λ x2 x3 . cn) (λ x2 x3 . ccom (cv x1) (cmpt2 (λ x4 x5 . cn) (λ x4 x5 . cn) (λ x4 x5 . cop (cif (wbr (cv x4) (cv x2) clt) (cv x4) (co (cv x4) c1 caddc)) (cif (wbr (cv x5) (cv x3) clt) (cv x5) (co (cv x5) c1 caddc))))))) ⟶ x0) ⟶ x0
Axiom df_lmat__df_cref__df_ldlf__df_pcmp__df_metid__df_pstm__df_hcmp__df_qqh__df_rrh__df_rrext__df_xrh__df_mntop__df_ind__df_esum__df_ofc__df_siga__df_sigagen__df_brsiga : ∀ x0 : ο . (wceq clmat (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . co c1 (cfv (cv x1) chash) cfz) (λ x2 x3 . co c1 (cfv (cfv cc0 (cv x1)) chash) cfz) (λ x2 x3 . cfv (co (cv x3) c1 cmin) (cfv (co (cv x2) c1 cmin) (cv x1))))) ⟶ (∀ x1 : ι → ο . wceq (ccref x1) (crab (λ x2 . wral (λ x3 . wceq (cuni (cv x2)) (cuni (cv x3)) ⟶ wrex (λ x4 . wbr (cv x4) (cv x3) cref) (λ x4 . cin (cpw (cv x2)) x1)) (λ x3 . cpw (cv x2))) (λ x2 . ctop))) ⟶ wceq cldlf (ccref (cab (λ x1 . wbr (cv x1) com cdom))) ⟶ wceq cpcmp (cab (λ x1 . wcel (cv x1) (ccref (cfv (cv x1) clocfin)))) ⟶ wceq cmetid (cmpt (λ x1 . cuni (crn cpsmet)) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (cdm (cdm (cv x1)))) (wcel (cv x3) (cdm (cdm (cv x1))))) (wceq (co (cv x2) (cv x3) (cv x1)) cc0)))) ⟶ wceq cpstm (cmpt (λ x1 . cuni (crn cpsmet)) (λ x1 . cmpt2 (λ x2 x3 . cqs (cdm (cdm (cv x1))) (cfv (cv x1) cmetid)) (λ x2 x3 . cqs (cdm (cdm (cv x1))) (cfv (cv x1) cmetid)) (λ x2 x3 . cuni (cab (λ x4 . wrex (λ x5 . wrex (λ x6 . wceq (cv x4) (co (cv x5) (cv x6) (cv x1))) (λ x6 . cv x3)) (λ x5 . cv x2)))))) ⟶ wceq chcmp (copab (λ x1 x2 . w3a (wa (wcel (cv x1) (cuni (crn cust))) (wcel (cv x2) ccusp)) (wceq (co (cfv (cv x2) cuss) (cdm (cuni (cv x1))) crest) (cv x1)) (wceq (cfv (cdm (cuni (cv x1))) (cfv (cfv (cv x2) ctopn) ccl)) (cfv (cv x2) cbs)))) ⟶ wceq cqqh (cmpt (λ x1 . cvv) (λ x1 . crn (cmpt2 (λ x2 x3 . cz) (λ x2 x3 . cima (ccnv (cfv (cv x1) czrh)) (cfv (cv x1) cui)) (λ x2 x3 . cop (co (cv x2) (cv x3) cdiv) (co (cfv (cv x2) (cfv (cv x1) czrh)) (cfv (cv x3) (cfv (cv x1) czrh)) (cfv (cv x1) cdvr)))))) ⟶ wceq crrh (cmpt (λ x1 . cvv) (λ x1 . cfv (cfv (cv x1) cqqh) (co (cfv (crn cioo) ctg) (cfv (cv x1) ctopn) ccnext))) ⟶ wceq crrext (crab (λ x1 . wa (wa (wcel (cfv (cv x1) czlm) cnlm) (wceq (cfv (cv x1) cchr) cc0)) (wa (wcel (cv x1) ccusp) (wceq (cfv (cv x1) cuss) (cfv (cres (cfv (cv x1) cds) (cxp (cfv (cv x1) cbs) (cfv (cv x1) cbs))) cmetu)))) (λ x1 . cin cnrg cdr)) ⟶ wceq cxrh (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cxr) (λ x2 . cif (wcel (cv x2) cr) (cfv (cv x2) (cfv (cv x1) crrh)) (cif (wceq (cv x2) cpnf) (cfv (cima (cfv (cv x1) crrh) cr) (cfv (cv x1) club)) (cfv (cima (cfv (cv x1) crrh) cr) (cfv (cv x1) cglb)))))) ⟶ wceq cmntop (copab (λ x1 x2 . wa (wcel (cv x1) cn0) (w3a (wcel (cv x2) c2ndc) (wcel (cv x2) cha) (wcel (cv x2) (clly (cec (cfv (cfv (cv x1) cehl) ctopn) chmph)))))) ⟶ wceq cind (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cv x1)) (λ x2 . cmpt (λ x3 . cv x1) (λ x3 . cif (wcel (cv x3) (cv x2)) c1 cc0)))) ⟶ (∀ x1 x2 : ι → ι → ο . wceq (cesum x1 x2) (cuni (co (co cxrs (co cc0 cpnf cicc) cress) (cmpt x1 x2) ctsu))) ⟶ (∀ x1 : ι → ο . wceq (cofc x1) (cmpt2 (λ x2 x3 . cvv) (λ x2 x3 . cvv) (λ x2 x3 . cmpt (λ x4 . cdm (cv x2)) (λ x4 . co (cfv (cv x4) (cv x2)) (cv x3) x1)))) ⟶ wceq csiga (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wa (wss (cv x2) (cpw (cv x1))) (w3a (wcel (cv x1) (cv x2)) (wral (λ x3 . wcel (cdif (cv x1) (cv x3)) (cv x2)) (λ x3 . cv x2)) (wral (λ x3 . wbr (cv x3) com cdom ⟶ wcel (cuni (cv x3)) (cv x2)) (λ x3 . cpw (cv x2))))))) ⟶ wceq csigagen (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wss (cv x1) (cv x2)) (λ x2 . cfv (cuni (cv x1)) csiga)))) ⟶ wceq cbrsiga (cfv (cfv (crn cioo) ctg) csigagen) ⟶ x0) ⟶ x0
Axiom df_sx__df_meas__df_dde__df_ae__df_fae__df_mbfm__df_oms__df_carsg__df_sitg__df_sitm__df_itgm__df_sseq__df_fib__df_prob__df_cndprob__df_rrv__df_orvc__df_repr : ∀ x0 : ο . (wceq csx (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cfv (crn (cmpt2 (λ x3 x4 . cv x1) (λ x3 x4 . cv x2) (λ x3 x4 . cxp (cv x3) (cv x4)))) csigagen)) ⟶ wceq cmeas (cmpt (λ x1 . cuni (crn csiga)) (λ x1 . cab (λ x2 . w3a (wf (cv x1) (co cc0 cpnf cicc) (cv x2)) (wceq (cfv c0 (cv x2)) cc0) (wral (λ x3 . wa (wbr (cv x3) com cdom) (wdisj (λ x4 . cv x3) cv) ⟶ wceq (cfv (cuni (cv x3)) (cv x2)) (cesum (λ x4 . cv x3) (λ x4 . cfv (cv x4) (cv x2)))) (λ x3 . cpw (cv x1)))))) ⟶ wceq cdde (cmpt (λ x1 . cpw cr) (λ x1 . cif (wcel cc0 (cv x1)) c1 cc0)) ⟶ wceq cae (copab (λ x1 x2 . wceq (cfv (cdif (cuni (cdm (cv x2))) (cv x1)) (cv x2)) cc0)) ⟶ wceq cfae (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cuni (crn cmeas)) (λ x1 x2 . copab (λ x3 x4 . wa (wa (wcel (cv x3) (co (cdm (cv x1)) (cuni (cdm (cv x2))) cmap)) (wcel (cv x4) (co (cdm (cv x1)) (cuni (cdm (cv x2))) cmap))) (wbr (crab (λ x5 . wbr (cfv (cv x5) (cv x3)) (cfv (cv x5) (cv x4)) (cv x1)) (λ x5 . cuni (cdm (cv x2)))) (cv x2) cae)))) ⟶ wceq cmbfm (cmpt2 (λ x1 x2 . cuni (crn csiga)) (λ x1 x2 . cuni (crn csiga)) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wcel (cima (ccnv (cv x3)) (cv x4)) (cv x1)) (λ x4 . cv x2)) (λ x3 . co (cuni (cv x2)) (cuni (cv x1)) cmap))) ⟶ wceq coms (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cuni (cdm (cv x1)))) (λ x2 . cinf (crn (cmpt (λ x3 . crab (λ x4 . wa (wss (cv x2) (cuni (cv x4))) (wbr (cv x4) com cdom)) (λ x4 . cpw (cdm (cv x1)))) (λ x3 . cesum (λ x4 . cv x3) (λ x4 . cfv (cv x4) (cv x1))))) (co cc0 cpnf cicc) clt))) ⟶ wceq ccarsg (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wceq (co (cfv (cin (cv x3) (cv x2)) (cv x1)) (cfv (cdif (cv x3) (cv x2)) (cv x1)) cxad) (cfv (cv x3) (cv x1))) (λ x3 . cpw (cuni (cdm (cv x1))))) (λ x2 . cpw (cuni (cdm (cv x1)))))) ⟶ wceq csitg (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cuni (crn cmeas)) (λ x1 x2 . cmpt (λ x3 . crab (λ x4 . wa (wcel (crn (cv x4)) cfn) (wral (λ x5 . wcel (cfv (cima (ccnv (cv x4)) (csn (cv x5))) (cv x2)) (co cc0 cpnf cico)) (λ x5 . cdif (crn (cv x4)) (csn (cfv (cv x1) c0g))))) (λ x4 . co (cdm (cv x2)) (cfv (cfv (cv x1) ctopn) csigagen) cmbfm)) (λ x3 . co (cv x1) (cmpt (λ x4 . cdif (crn (cv x3)) (csn (cfv (cv x1) c0g))) (λ x4 . co (cfv (cfv (cima (ccnv (cv x3)) (csn (cv x4))) (cv x2)) (cfv (cfv (cv x1) csca) crrh)) (cv x4) (cfv (cv x1) cvsca))) cgsu))) ⟶ wceq csitm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cuni (crn cmeas)) (λ x1 x2 . cmpt2 (λ x3 x4 . cdm (co (cv x1) (cv x2) csitg)) (λ x3 x4 . cdm (co (cv x1) (cv x2) csitg)) (λ x3 x4 . cfv (co (cv x3) (cv x4) (cof (cfv (cv x1) cds))) (co (co cxrs (co cc0 cpnf cicc) cress) (cv x2) csitg)))) ⟶ wceq citgm (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cuni (crn cmeas)) (λ x1 x2 . cfv (co (cv x1) (cv x2) csitg) (co (cfv (co (cv x1) (cv x2) csitm) cmetu) (cfv (cv x1) cuss) ccnext))) ⟶ wceq csseq (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cun (cv x1) (ccom clsw (cseq (cmpt2 (λ x3 x4 . cvv) (λ x3 x4 . cvv) (λ x3 x4 . co (cv x3) (cs1 (cfv (cv x3) (cv x2))) cconcat)) (cxp cn0 (csn (co (cv x1) (cs1 (cfv (cv x1) (cv x2))) cconcat))) (cfv (cv x1) chash))))) ⟶ wceq cfib (co (cs2 cc0 c1) (cmpt (λ x1 . cin (cword cn0) (cima (ccnv chash) (cfv c2 cuz))) (λ x1 . co (cfv (co (cfv (cv x1) chash) c2 cmin) (cv x1)) (cfv (co (cfv (cv x1) chash) c1 cmin) (cv x1)) caddc)) csseq) ⟶ wceq cprb (crab (λ x1 . wceq (cfv (cuni (cdm (cv x1))) (cv x1)) c1) (λ x1 . cuni (crn cmeas))) ⟶ wceq ccprob (cmpt (λ x1 . cprb) (λ x1 . cmpt2 (λ x2 x3 . cdm (cv x1)) (λ x2 x3 . cdm (cv x1)) (λ x2 x3 . co (cfv (cin (cv x2) (cv x3)) (cv x1)) (cfv (cv x3) (cv x1)) cdiv))) ⟶ wceq crrv (cmpt (λ x1 . cprb) (λ x1 . co (cdm (cv x1)) cbrsiga cmbfm)) ⟶ (∀ x1 : ι → ο . wceq (corvc x1) (cmpt2 (λ x2 x3 . cab (λ x4 . wfun (cv x4))) (λ x2 x3 . cvv) (λ x2 x3 . cima (ccnv (cv x2)) (cab (λ x4 . wbr (cv x4) (cv x3) x1))))) ⟶ wceq crepr (cmpt (λ x1 . cn0) (λ x1 . cmpt2 (λ x2 x3 . cpw cn) (λ x2 x3 . cz) (λ x2 x3 . crab (λ x4 . wceq (csu (co cc0 (cv x1) cfzo) (λ x5 . cfv (cv x5) (cv x4))) (cv x3)) (λ x4 . co (cv x2) (co cc0 (cv x1) cfzo) cmap)))) ⟶ x0) ⟶ x0
Axiom df_vts__ax_hgt749__ax_ros335__ax_ros336__df_trkg2d__df_afs__df_bnj17__df_bnj14__df_bnj13__df_bnj15__df_bnj18__df_bnj19__ax_7d__ax_8d__ax_9d1__ax_9d2__ax_10d__ax_11d : ∀ x0 : ο . (wceq cvts (cmpt2 (λ x1 x2 . co cc cn cmap) (λ x1 x2 . cn0) (λ x1 x2 . cmpt (λ x3 . cc) (λ x3 . csu (co c1 (cv x2) cfz) (λ x4 . co (cfv (cv x4) (cv x1)) (cfv (co (co ci (co c2 cpi cmul) cmul) (co (cv x4) (cv x3) cmul) cmul) ce) cmul)))) ⟶ wral (λ x1 . wbr (co (cdc c1 cc0) (cdc c2 c7) cexp) (cv x1) cle ⟶ wrex (λ x2 . wrex (λ x3 . w3a (wral (λ x4 . wbr (cfv (cv x4) (cv x3)) (co c1 (cdp2 cc0 (cdp2 c7 (cdp2 c9 (cdp2 c9 (cdp2 c5 c5))))) cdp) cle) (λ x4 . cn)) (wral (λ x4 . wbr (cfv (cv x4) (cv x2)) (co c1 (cdp2 c4 (cdp2 c1 c4)) cdp) cle) (λ x4 . cn)) (wbr (co (co cc0 (cdp2 cc0 (cdp2 cc0 (cdp2 cc0 (cdp2 c4 (cdp2 c2 (cdp2 c2 (cdp2 c4 c8))))))) cdp) (co (cv x1) c2 cexp) cmul) (citg (λ x4 . co cc0 c1 cioo) (λ x4 . co (co (cfv (cv x4) (co (co cvma (cv x2) (cof cmul)) (cv x1) cvts)) (co (cfv (cv x4) (co (co cvma (cv x3) (cof cmul)) (cv x1) cvts)) c2 cexp) cmul) (cfv (co (co ci (co c2 cpi cmul) cmul) (co (cneg (cv x1)) (cv x4) cmul) cmul) ce) cmul)) cle)) (λ x3 . co (co cc0 cpnf cico) cn cmap)) (λ x2 . co (co cc0 cpnf cico) cn cmap)) (λ x1 . crab (λ x2 . wn (wbr c2 (cv x2) cdvds)) (λ x2 . cz)) ⟶ wral (λ x1 . wbr (cfv (cv x1) cchp) (co (co c1 (cdp2 cc0 (cdp2 c3 (cdp2 c8 (cdp2 c8 c3)))) cdp) (cv x1) cmul) clt) (λ x1 . crp) ⟶ wral (λ x1 . wbr (co (cfv (cv x1) cchp) (cfv (cv x1) ccht) cmin) (co (co c1 (cdp2 c4 (cdp2 c2 (cdp2 c6 c2))) cdp) (cfv (cv x1) csqrt) cmul) clt) (λ x1 . crp) ⟶ wceq cstrkg2d (cab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wa (wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . wn (w3o (wcel (cv x7) (co (cv x5) (cv x6) (cv x4))) (wcel (cv x5) (co (cv x7) (cv x6) (cv x4))) (wcel (cv x6) (co (cv x5) (cv x7) (cv x4))))) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (wral (λ x5 . wral (λ x6 . wral (λ x7 . wral (λ x8 . wral (λ x9 . wa (w3a (wceq (co (cv x5) (cv x8) (cv x3)) (co (cv x5) (cv x9) (cv x3))) (wceq (co (cv x6) (cv x8) (cv x3)) (co (cv x6) (cv x9) (cv x3))) (wceq (co (cv x7) (cv x8) (cv x3)) (co (cv x7) (cv x9) (cv x3)))) (wne (cv x8) (cv x9)) ⟶ w3o (wcel (cv x7) (co (cv x5) (cv x6) (cv x4))) (wcel (cv x5) (co (cv x7) (cv x6) (cv x4))) (wcel (cv x6) (co (cv x5) (cv x7) (cv x4)))) (λ x9 . cv x2)) (λ x8 . cv x2)) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2))) (cfv (cv x1) citv)) (cfv (cv x1) cds)) (cfv (cv x1) cbs))) ⟶ wceq cafs (cmpt (λ x1 . cstrkg) (λ x1 . copab (λ x2 x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . wrex (λ x12 . wrex (λ x13 . wrex (λ x14 . w3a (wceq (cv x2) (cop (cop (cv x7) (cv x8)) (cop (cv x9) (cv x10)))) (wceq (cv x3) (cop (cop (cv x11) (cv x12)) (cop (cv x13) (cv x14)))) (w3a (wa (wcel (cv x8) (co (cv x7) (cv x9) (cv x6))) (wcel (cv x12) (co (cv x11) (cv x13) (cv x6)))) (wa (wceq (co (cv x7) (cv x8) (cv x5)) (co (cv x11) (cv x12) (cv x5))) (wceq (co (cv x8) (cv x9) (cv x5)) (co (cv x12) (cv x13) (cv x5)))) (wa (wceq (co (cv x7) (cv x10) (cv x5)) (co (cv x11) (cv x14) (cv x5))) (wceq (co (cv x8) (cv x10) (cv x5)) (co (cv x12) (cv x14) (cv x5)))))) (λ x14 . cv x4)) (λ x13 . cv x4)) (λ x12 . cv x4)) (λ x11 . cv x4)) (λ x10 . cv x4)) (λ x9 . cv x4)) (λ x8 . cv x4)) (λ x7 . cv x4)) (cfv (cv x1) citv)) (cfv (cv x1) cds)) (cfv (cv x1) cbs)))) ⟶ (∀ x1 x2 x3 x4 : ο . wb (w_bnj17 x1 x2 x3 x4) (wa (w3a x1 x2 x3) x4)) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (c_bnj14 x1 x2 x3) (crab (λ x4 . wbr (cv x4) x3 x2) (λ x4 . x1))) ⟶ (∀ x1 x2 : ι → ο . wb (w_bnj13 x1 x2) (wral (λ x3 . wcel (c_bnj14 x1 x2 (cv x3)) cvv) (λ x3 . x1))) ⟶ (∀ x1 x2 : ι → ο . wb (w_bnj15 x1 x2) (wa (wfr x1 x2) (w_bnj13 x1 x2))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (c_bnj18 x1 x2 x3) (ciun (λ x4 . cab (λ x5 . wrex (λ x6 . w3a (wfn (cv x5) (cv x6)) (wceq (cfv c0 (cv x5)) (c_bnj14 x1 x2 x3)) (wral (λ x7 . wcel (csuc (cv x7)) (cv x6) ⟶ wceq (cfv (csuc (cv x7)) (cv x5)) (ciun (λ x8 . cfv (cv x7) (cv x5)) (λ x8 . c_bnj14 x1 x2 (cv x8)))) (λ x7 . com))) (λ x6 . cdif com (csn c0)))) (λ x4 . ciun (λ x5 . cdm (cv x4)) (λ x5 . cfv (cv x5) (cv x4))))) ⟶ (∀ x1 x2 x3 : ι → ο . wb (w_bnj19 x1 x2 x3) (wral (λ x4 . wss (c_bnj14 x1 x3 (cv x4)) x2) (λ x4 . x2))) ⟶ (∀ x1 : ι → ι → ο . (∀ x2 x3 . x1 x2 x3) ⟶ ∀ x2 x3 . x1 x3 x2) ⟶ (∀ x1 x2 x3 . wceq (cv x1) (cv x2) ⟶ wceq (cv x1) (cv x3) ⟶ wceq (cv x2) (cv x3)) ⟶ wn (∀ x1 . wn (wceq (cv x1) (cv x1))) ⟶ (∀ x1 . wn (∀ x2 . wn (wceq (cv x2) (cv x1)))) ⟶ (∀ x1 x2 . (∀ x3 . wceq (cv x3) (cv x2)) ⟶ ∀ x3 . wceq (cv x3) (cv x1)) ⟶ (∀ x1 : ι → ι → ο . ∀ x2 x3 . wceq (cv x2) (cv x3) ⟶ (∀ x4 . x1 x2 x4) ⟶ ∀ x4 . wceq (cv x4) (cv x3) ⟶ x1 x4 x3) ⟶ x0) ⟶ x0
Axiom df_retr__df_pconn__df_sconn__df_cvm__df_goel__df_gona__df_goal__df_sat__df_sate__df_fmla__df_gonot__df_goan__df_goim__df_goor__df_gobi__df_goeq__df_goex__df_prv : ∀ x0 : ο . (wceq cretr (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . crab (λ x3 . wrex (λ x4 . wne (co (ccom (cv x3) (cv x4)) (cres cid (cuni (cv x1))) (co (cv x1) (cv x1) chtpy)) c0) (λ x4 . co (cv x2) (cv x1) ccn)) (λ x3 . co (cv x1) (cv x2) ccn))) ⟶ wceq cpconn (crab (λ x1 . wral (λ x2 . wral (λ x3 . wrex (λ x4 . wa (wceq (cfv cc0 (cv x4)) (cv x2)) (wceq (cfv c1 (cv x4)) (cv x3))) (λ x4 . co cii (cv x1) ccn)) (λ x3 . cuni (cv x1))) (λ x2 . cuni (cv x1))) (λ x1 . ctop)) ⟶ wceq csconn (crab (λ x1 . wral (λ x2 . wceq (cfv cc0 (cv x2)) (cfv c1 (cv x2)) ⟶ wbr (cv x2) (cxp (co cc0 c1 cicc) (csn (cfv cc0 (cv x2)))) (cfv (cv x1) cphtpc)) (λ x2 . co cii (cv x1) ccn)) (λ x1 . cpconn)) ⟶ wceq ccvm (cmpt2 (λ x1 x2 . ctop) (λ x1 x2 . ctop) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wrex (λ x5 . wa (wcel (cv x4) (cv x5)) (wrex (λ x6 . wa (wceq (cuni (cv x6)) (cima (ccnv (cv x3)) (cv x5))) (wral (λ x7 . wa (wral (λ x8 . wceq (cin (cv x7) (cv x8)) c0) (λ x8 . cdif (cv x6) (csn (cv x7)))) (wcel (cres (cv x3) (cv x7)) (co (co (cv x1) (cv x7) crest) (co (cv x2) (cv x5) crest) chmeo))) (λ x7 . cv x6))) (λ x6 . cdif (cpw (cv x1)) (csn c0)))) (λ x5 . cv x2)) (λ x4 . cuni (cv x2))) (λ x3 . co (cv x1) (cv x2) ccn))) ⟶ wceq cgoe (cmpt (λ x1 . cxp com com) (λ x1 . cop c0 (cv x1))) ⟶ wceq cgna (cmpt (λ x1 . cxp cvv cvv) (λ x1 . cop c1o (cv x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (cgol x1 x2) (cop c2o (cop x2 x1))) ⟶ wceq csat (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cres (crdg (cmpt (λ x3 . cvv) (λ x3 . cun (cv x3) (copab (λ x4 x5 . wrex (λ x6 . wo (wrex (λ x7 . wa (wceq (cv x4) (co (cfv (cv x6) c1st) (cfv (cv x7) c1st) cgna)) (wceq (cv x5) (cdif (co (cv x1) com cmap) (cin (cfv (cv x6) c2nd) (cfv (cv x7) c2nd))))) (λ x7 . cv x3)) (wrex (λ x7 . wa (wceq (cv x4) (cgol (cfv (cv x6) c1st) (cv x7))) (wceq (cv x5) (crab (λ x8 . wral (λ x9 . wcel (cun (csn (cop (cv x7) (cv x9))) (cres (cv x8) (cdif com (csn (cv x7))))) (cfv (cv x6) c2nd)) (λ x9 . cv x1)) (λ x8 . co (cv x1) com cmap)))) (λ x7 . com))) (λ x6 . cv x3))))) (copab (λ x3 x4 . wrex (λ x5 . wrex (λ x6 . wa (wceq (cv x3) (co (cv x5) (cv x6) cgoe)) (wceq (cv x4) (crab (λ x7 . wbr (cfv (cv x5) (cv x7)) (cfv (cv x6) (cv x7)) (cv x2)) (λ x7 . co (cv x1) com cmap)))) (λ x6 . com)) (λ x5 . com)))) (csuc com))) ⟶ wceq csate (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cfv (cv x2) (cfv com (co (cv x1) (cin cep (cxp (cv x1) (cv x1))) csat)))) ⟶ wceq cfmla (cmpt (λ x1 . csuc com) (λ x1 . cdm (cfv (cv x1) (co c0 c0 csat)))) ⟶ (∀ x1 : ι → ο . wceq (cgon x1) (co x1 x1 cgna)) ⟶ wceq cgoa (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cgon (co (cv x1) (cv x2) cgna))) ⟶ wceq cgoi (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cv x1) (cgon (cv x2)) cgna)) ⟶ wceq cgoo (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cgon (cv x1)) (cv x2) cgoi)) ⟶ wceq cgob (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (co (cv x1) (cv x2) cgoi) (co (cv x2) (cv x1) cgoi) cgoa)) ⟶ wceq cgoq (cmpt2 (λ x1 x2 . com) (λ x1 x2 . com) (λ x1 x2 . csb (csuc (cun (cv x1) (cv x2))) (λ x3 . cgol (co (co (cv x3) (cv x1) cgoe) (co (cv x3) (cv x2) cgoe) cgob) (cv x3)))) ⟶ (∀ x1 x2 : ι → ο . wceq (cgox x1 x2) (cgon (cgol (cgon x1) x2))) ⟶ wceq cprv (copab (λ x1 x2 . wceq (co (cv x1) (cv x2) csate) (co (cv x1) com cmap))) ⟶ x0) ⟶ x0
Axiom df_gzext__df_gzrep__df_gzpow__df_gzun__df_gzreg__df_gzinf__df_gzf__df_mcn__df_mvar__df_mty__df_mtc__df_mmax__df_mvt__df_mrex__df_mex__df_mdv__df_mvrs__df_mrsub : ∀ x0 : ο . (wceq cgze (co (cgol (co (co c2o c0 cgoe) (co c2o c1o cgoe) cgob) c2o) (co c0 c1o cgoq) cgoi) ⟶ wceq cgzr (cmpt (λ x1 . cfv com cfmla) (λ x1 . co (cgol (cgox (cgol (co (cgol (cv x1) c1o) (co c2o c1o cgoq) cgoi) c2o) c1o) c3o) (cgol (cgol (co (co c2o c1o cgoe) (cgox (co (co c3o c0 cgoe) (cgol (cv x1) c1o) cgoa) c3o) cgob) c2o) c1o) cgoi)) ⟶ wceq cgzp (cgox (cgol (co (cgol (co (co c1o c2o cgoe) (co c1o c0 cgoe) cgob) c1o) (co c2o c1o cgoe) cgoi) c2o) c1o) ⟶ wceq cgzu (cgox (cgol (co (cgox (co (co c2o c1o cgoe) (co c1o c0 cgoe) cgoa) c1o) (co c2o c1o cgoe) cgoi) c2o) c1o) ⟶ wceq cgzg (co (cgox (co c1o c0 cgoe) c1o) (cgox (co (co c1o c0 cgoe) (cgol (co (co c2o c1o cgoe) (cgon (co c2o c0 cgoe)) cgoi) c2o) cgoa) c1o) cgoi) ⟶ wceq cgzi (cgox (co (co c0 c1o cgoe) (cgol (co (co c2o c1o cgoe) (cgox (co (co c2o c0 cgoe) (co c0 c1o cgoe) cgoa) c0) cgoi) c2o) cgoa) c1o) ⟶ wceq cgzf (cab (λ x1 . w3a (w3a (wtr (cv x1)) (wbr (cv x1) cgze cprv) (wbr (cv x1) cgzp cprv)) (w3a (wbr (cv x1) cgzu cprv) (wbr (cv x1) cgzg cprv) (wbr (cv x1) cgzi cprv)) (wral (λ x2 . wbr (cv x1) (cfv (cv x2) cgzr) cprv) (λ x2 . cfv com cfmla)))) ⟶ wceq cmcn (cslot c1) ⟶ wceq cmvar (cslot c2) ⟶ wceq cmty (cslot c3) ⟶ wceq cmtc (cslot c4) ⟶ wceq cmax (cslot c5) ⟶ wceq cmvt (cmpt (λ x1 . cvv) (λ x1 . crn (cfv (cv x1) cmty))) ⟶ wceq cmrex (cmpt (λ x1 . cvv) (λ x1 . cword (cun (cfv (cv x1) cmcn) (cfv (cv x1) cmvar)))) ⟶ wceq cmex (cmpt (λ x1 . cvv) (λ x1 . cxp (cfv (cv x1) cmtc) (cfv (cv x1) cmrex))) ⟶ wceq cmdv (cmpt (λ x1 . cvv) (λ x1 . cdif (cxp (cfv (cv x1) cmvar) (cfv (cv x1) cmvar)) cid)) ⟶ wceq cmvrs (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmex) (λ x2 . cin (crn (cfv (cv x2) c2nd)) (cfv (cv x1) cmvar)))) ⟶ wceq cmrsub (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . co (cfv (cv x1) cmrex) (cfv (cv x1) cmvar) cpm) (λ x2 . cmpt (λ x3 . cfv (cv x1) cmrex) (λ x3 . co (cfv (cun (cfv (cv x1) cmcn) (cfv (cv x1) cmvar)) cfrmd) (ccom (cmpt (λ x4 . cun (cfv (cv x1) cmcn) (cfv (cv x1) cmvar)) (λ x4 . cif (wcel (cv x4) (cdm (cv x2))) (cfv (cv x4) (cv x2)) (cs1 (cv x4)))) (cv x3)) cgsu)))) ⟶ x0) ⟶ x0
Axiom df_msub__df_mvh__df_mpst__df_msr__df_msta__df_mfs__df_mcls__df_mpps__df_mthm__df_m0s__df_msa__df_mwgfs__df_msyn__df_mtree__df_mst__df_msax__df_mufs__df_muv : ∀ x0 : ο . (wceq cmsub (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . co (cfv (cv x1) cmrex) (cfv (cv x1) cmvar) cpm) (λ x2 . cmpt (λ x3 . cfv (cv x1) cmex) (λ x3 . cop (cfv (cv x3) c1st) (cfv (cfv (cv x3) c2nd) (cfv (cv x2) (cfv (cv x1) cmrsub))))))) ⟶ wceq cmvh (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmvar) (λ x2 . cop (cfv (cv x2) (cfv (cv x1) cmty)) (cs1 (cv x2))))) ⟶ wceq cmpst (cmpt (λ x1 . cvv) (λ x1 . cxp (cxp (crab (λ x2 . wceq (ccnv (cv x2)) (cv x2)) (λ x2 . cpw (cfv (cv x1) cmdv))) (cin (cpw (cfv (cv x1) cmex)) cfn)) (cfv (cv x1) cmex))) ⟶ wceq cmsr (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmpst) (λ x2 . csb (cfv (cfv (cv x2) c1st) c2nd) (λ x3 . csb (cfv (cv x2) c2nd) (λ x4 . cotp (cin (cfv (cfv (cv x2) c1st) c1st) (csb (cuni (cima (cfv (cv x1) cmvrs) (cun (cv x3) (csn (cv x4))))) (λ x5 . cxp (cv x5) (cv x5)))) (cv x3) (cv x4)))))) ⟶ wceq cmsta (cmpt (λ x1 . cvv) (λ x1 . crn (cfv (cv x1) cmsr))) ⟶ wceq cmfs (cab (λ x1 . wa (wa (wceq (cin (cfv (cv x1) cmcn) (cfv (cv x1) cmvar)) c0) (wf (cfv (cv x1) cmvar) (cfv (cv x1) cmtc) (cfv (cv x1) cmty))) (wa (wss (cfv (cv x1) cmax) (cfv (cv x1) cmsta)) (wral (λ x2 . wn (wcel (cima (ccnv (cfv (cv x1) cmty)) (csn (cv x2))) cfn)) (λ x2 . cfv (cv x1) cmvt))))) ⟶ wceq cmcls (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cpw (cfv (cv x1) cmdv)) (λ x2 x3 . cpw (cfv (cv x1) cmex)) (λ x2 x3 . cint (cab (λ x4 . wa (wss (cun (cv x3) (crn (cfv (cv x1) cmvh))) (cv x4)) (∀ x5 x6 x7 . wcel (cotp (cv x5) (cv x6) (cv x7)) (cfv (cv x1) cmax) ⟶ wral (λ x8 . wa (wss (cima (cv x8) (cun (cv x6) (crn (cfv (cv x1) cmvh)))) (cv x4)) (∀ x9 x10 . wbr (cv x9) (cv x10) (cv x5) ⟶ wss (cxp (cfv (cfv (cfv (cv x9) (cfv (cv x1) cmvh)) (cv x8)) (cfv (cv x1) cmvrs)) (cfv (cfv (cfv (cv x10) (cfv (cv x1) cmvh)) (cv x8)) (cfv (cv x1) cmvrs))) (cv x2)) ⟶ wcel (cfv (cv x7) (cv x8)) (cv x4)) (λ x8 . crn (cfv (cv x1) cmsub)))))))) ⟶ wceq cmpps (cmpt (λ x1 . cvv) (λ x1 . coprab (λ x2 x3 x4 . wa (wcel (cotp (cv x2) (cv x3) (cv x4)) (cfv (cv x1) cmpst)) (wcel (cv x4) (co (cv x2) (cv x3) (cfv (cv x1) cmcls)))))) ⟶ wceq cmthm (cmpt (λ x1 . cvv) (λ x1 . cima (ccnv (cfv (cv x1) cmsr)) (cima (cfv (cv x1) cmsr) (cfv (cv x1) cmpps)))) ⟶ wceq cm0s (cmpt (λ x1 . cvv) (λ x1 . cotp c0 c0 (cv x1))) ⟶ wceq cmsa (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . w3a (wcel (cfv (cv x2) cm0s) (cfv (cv x1) cmax)) (wcel (cfv (cv x2) c1st) (cfv (cv x1) cmvt)) (wfun (cres (ccnv (cfv (cv x2) c2nd)) (cfv (cv x1) cmvar)))) (λ x2 . cfv (cv x1) cmex))) ⟶ wceq cmwgfs (crab (λ x1 . ∀ x2 x3 x4 . wa (wcel (cotp (cv x2) (cv x3) (cv x4)) (cfv (cv x1) cmax)) (wcel (cfv (cv x4) c1st) (cfv (cv x1) cmvt)) ⟶ wrex (λ x5 . wcel (cv x4) (cima (cv x5) (cfv (cv x1) cmsa))) (λ x5 . crn (cfv (cv x1) cmsub))) (λ x1 . cmfs)) ⟶ wceq cmsy (cslot c6) ⟶ wceq cmtree (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cpw (cfv (cv x1) cmdv)) (λ x2 x3 . cpw (cfv (cv x1) cmex)) (λ x2 x3 . cint (cab (λ x4 . w3a (wral (λ x5 . wbr (cv x5) (cop (cfv (cv x5) cm0s) c0) (cv x4)) (λ x5 . crn (cfv (cv x1) cmvh))) (wral (λ x5 . wbr (cv x5) (cop (cfv (cotp (cv x2) (cv x3) (cv x5)) (cfv (cv x1) cmsr)) c0) (cv x4)) (λ x5 . cv x3)) (∀ x5 x6 x7 . wcel (cotp (cv x5) (cv x6) (cv x7)) (cfv (cv x1) cmax) ⟶ wral (λ x8 . (∀ x9 x10 . wbr (cv x9) (cv x10) (cv x5) ⟶ wss (cxp (cfv (cfv (cfv (cv x9) (cfv (cv x1) cmvh)) (cv x8)) (cfv (cv x1) cmvrs)) (cfv (cfv (cfv (cv x10) (cfv (cv x1) cmvh)) (cv x8)) (cfv (cv x1) cmvrs))) (cv x2)) ⟶ wss (cxp (csn (cfv (cv x7) (cv x8))) (cixp (λ x9 . cun (cv x6) (cima (cfv (cv x1) cmvh) (cuni (cima (cfv (cv x1) cmvrs) (cun (cv x6) (csn (cv x7))))))) (λ x9 . cima (cv x4) (csn (cfv (cv x9) (cv x8)))))) (cv x4)) (λ x8 . crn (cfv (cv x1) cmsub)))))))) ⟶ wceq cmst (cmpt (λ x1 . cvv) (λ x1 . cres (co c0 c0 (cfv (cv x1) cmtree)) (cres (cfv (cv x1) cmex) (cfv (cv x1) cmvt)))) ⟶ wceq cmsax (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmsa) (λ x2 . cima (cfv (cv x1) cmvh) (cfv (cv x2) (cfv (cv x1) cmvrs))))) ⟶ wceq cmufs (crab (λ x1 . wfun (cfv (cv x1) cmst)) (λ x1 . cmgfs)) ⟶ wceq cmuv (cslot c7) ⟶ x0) ⟶ x0
Axiom df_mfsh__df_mevl__df_mvl__df_mvsb__df_mfrel__df_mdl__df_musyn__df_gmdl__df_mitp__df_mfitp__df_irng__df_cplmet__df_homlimb__df_homlim__df_plfl__df_sfl1__df_sfl__df_psl : ∀ x0 : ο . (wceq cmfsh (cslot c8) ⟶ wceq cmevl (cslot c9) ⟶ wceq cmvl (cmpt (λ x1 . cvv) (λ x1 . cixp (λ x2 . cfv (cv x1) cmvar) (λ x2 . cima (cfv (cv x1) cmuv) (csn (cfv (cv x2) (cfv (cv x1) cmty)))))) ⟶ wceq cmvsb (cmpt (λ x1 . cvv) (λ x1 . coprab (λ x2 x3 x4 . w3a (wa (wcel (cv x2) (crn (cfv (cv x1) cmsub))) (wcel (cv x3) (cfv (cv x1) cmvl))) (wral (λ x5 . wbr (cv x3) (cfv (cfv (cv x5) (cfv (cv x1) cmvh)) (cv x2)) (cdm (cfv (cv x1) cmevl))) (λ x5 . cfv (cv x1) cmvar)) (wceq (cv x4) (cmpt (λ x5 . cfv (cv x1) cmvar) (λ x5 . co (cv x3) (cfv (cfv (cv x5) (cfv (cv x1) cmvh)) (cv x2)) (cfv (cv x1) cmevl))))))) ⟶ wceq cmfr (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wceq (ccnv (cv x2)) (cv x2)) (wral (λ x3 . wral (λ x4 . wrex (λ x5 . wss (cv x4) (cima (cv x2) (csn (cv x5)))) (λ x5 . cima (cfv (cv x1) cmuv) (csn (cv x3)))) (λ x4 . cin (cpw (cfv (cv x1) cmuv)) cfn)) (λ x3 . cfv (cv x1) cmvt))) (λ x2 . cpw (cxp (cfv (cv x1) cmuv) (cfv (cv x1) cmuv))))) ⟶ wceq cmdl (crab (λ x1 . wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wa (w3a (wss (cv x2) (cxp (cfv (cv x1) cmtc) cvv)) (wcel (cv x6) (cfv (cv x1) cmfr)) (wcel (cv x5) (co (cv x2) (cxp (cv x4) (cfv (cv x1) cmex)) cpm))) (wral (λ x7 . wa (w3a (wral (λ x8 . wss (cima (cv x5) (csn (cop (cv x7) (cv x8)))) (cima (cv x2) (csn (cfv (cv x8) c1st)))) (λ x8 . cv x3)) (wral (λ x8 . wbr (cop (cv x7) (cfv (cv x8) (cfv (cv x1) cmvh))) (cfv (cv x8) (cv x7)) (cv x5)) (λ x8 . cfv (cv x1) cmvar)) (∀ x8 x9 x10 . wcel (cotp (cv x8) (cv x9) (cv x10)) (cfv (cv x1) cmax) ⟶ wa (∀ x11 x12 . wbr (cv x11) (cv x12) (cv x8) ⟶ wbr (cfv (cv x11) (cv x7)) (cfv (cv x12) (cv x7)) (cv x6)) (wss (cv x9) (cima (cdm (cv x5)) (csn (cv x7)))) ⟶ wbr (cv x7) (cv x10) (cdm (cv x5)))) (w3a (wral (λ x8 . wral (λ x9 . ∀ x10 . wbr (cop (cv x8) (cv x7)) (cv x10) (cfv (cv x1) cmvsb) ⟶ wceq (cima (cv x5) (csn (cop (cv x7) (cfv (cv x9) (cv x8))))) (cima (cv x5) (csn (cop (cv x10) (cv x9))))) (λ x9 . cfv (cv x1) cmex)) (λ x8 . crn (cfv (cv x1) cmsub))) (wral (λ x8 . wral (λ x9 . wceq (cres (cv x7) (cfv (cv x9) (cfv (cv x1) cmvrs))) (cres (cv x8) (cfv (cv x9) (cfv (cv x1) cmvrs))) ⟶ wceq (cima (cv x5) (csn (cop (cv x7) (cv x9)))) (cima (cv x5) (csn (cop (cv x8) (cv x9))))) (λ x9 . cv x3)) (λ x8 . cv x4)) (wral (λ x8 . wral (λ x9 . wss (cima (cv x7) (cfv (cv x9) (cfv (cv x1) cmvrs))) (cima (cv x6) (csn (cv x8))) ⟶ wss (cima (cv x5) (csn (cop (cv x7) (cv x9)))) (cima (cv x6) (csn (cv x8)))) (λ x9 . cv x3)) (λ x8 . cv x2)))) (λ x7 . cv x4))) (cfv (cv x1) cmfsh)) (cfv (cv x1) cmevl)) (cfv (cv x1) cmvl)) (cfv (cv x1) cmex)) (cfv (cv x1) cmuv)) (λ x1 . cmfs)) ⟶ wceq cusyn (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmuv) (λ x2 . cop (cfv (cfv (cv x2) c1st) (cfv (cv x1) cmsy)) (cfv (cv x2) c2nd)))) ⟶ (∀ x1 . wceq cgmdl (crab (λ x2 . w3a (wral (λ x3 . wss (cima (cfv (cv x2) cmuv) (csn (cv x3))) (cima (cfv (cv x2) cmuv) (csn (cfv (cv x3) (cfv (cv x2) cmsy))))) (λ x3 . cfv (cv x2) cmtc)) (wral (λ x3 . wral (λ x4 . wb (wbr (cv x3) (cv x4) (cfv (cv x2) cmfsh)) (wbr (cv x3) (cfv (cv x4) (cfv (cv x2) cusyn)) (cfv (cv x2) cmfsh))) (λ x4 . cfv (cv x1) cmuv)) (λ x3 . cfv (cv x1) cmuv)) (wral (λ x3 . wral (λ x4 . wceq (cima (cfv (cv x2) cmevl) (csn (cop (cv x3) (cv x4)))) (cin (cima (cfv (cv x2) cmevl) (csn (cop (cv x3) (cfv (cv x4) (cfv (cv x2) cmesy))))) (cima (cfv (cv x2) cmuv) (csn (cfv (cv x4) c1st))))) (λ x4 . cfv (cv x2) cmex)) (λ x3 . cfv (cv x2) cmvl))) (λ x2 . cin cmgfs cmdl))) ⟶ wceq cmitp (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cmsa) (λ x2 . cmpt (λ x3 . cixp (λ x4 . cfv (cv x2) (cfv (cv x1) cmvrs)) (λ x4 . cima (cfv (cv x1) cmuv) (csn (cfv (cv x4) (cfv (cv x1) cmty))))) (λ x3 . cio (λ x4 . wrex (λ x5 . wa (wceq (cv x3) (cres (cv x5) (cfv (cv x2) (cfv (cv x1) cmvrs)))) (wceq (cv x4) (co (cv x5) (cv x2) (cfv (cv x1) cmevl)))) (λ x5 . cfv (cv x1) cmvl)))))) ⟶ wceq cmfitp (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cixp (λ x3 . cfv (cv x1) cmsa) (λ x3 . co (cima (cfv (cv x1) cmuv) (csn (cfv (cv x3) (cfv (cv x1) c1st)))) (cixp (λ x4 . cfv (cv x3) (cfv (cv x1) cmvrs)) (λ x4 . cima (cfv (cv x1) cmuv) (csn (cfv (cv x4) (cfv (cv x1) cmty))))) cmap)) (λ x2 . crio (λ x3 . wral (λ x4 . w3a (wral (λ x5 . wbr (cop (cv x4) (cfv (cv x5) (cfv (cv x1) cmvh))) (cfv (cv x5) (cv x4)) (cv x3)) (λ x5 . cfv (cv x1) cmvar)) (∀ x5 x6 x7 . wbr (cv x5) (cop (cv x6) (cv x7)) (cfv (cv x1) cmst) ⟶ wbr (cop (cv x4) (cv x5)) (cfv (cmpt (λ x8 . cfv (cv x6) (cfv (cv x1) cmvrs)) (λ x8 . co (cv x4) (cfv (cfv (cv x8) (cfv (cv x1) cmvh)) (cv x7)) (cv x3))) (cv x2)) (cv x3)) (wral (λ x5 . wceq (cima (cv x3) (csn (cop (cv x4) (cv x5)))) (cin (cima (cv x3) (csn (cop (cv x4) (cfv (cv x5) (cfv (cv x1) cmesy))))) (cima (cfv (cv x1) cmuv) (csn (cfv (cv x5) c1st))))) (λ x5 . cfv (cv x1) cmex))) (λ x4 . cfv (cv x1) cmvl)) (λ x3 . co (cfv (cv x1) cmuv) (cxp (cfv (cv x1) cmvl) (cfv (cv x1) cmex)) cpm)))) ⟶ wceq citr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . ciun (λ x3 . cfv (co (cv x1) (cv x2) cress) cmn1) (λ x3 . cima (ccnv (cv x3)) (csn (cfv (cv x1) c0g))))) ⟶ wceq ccpms (cmpt (λ x1 . cvv) (λ x1 . csb (co (co (cv x1) cn cpws) (cfv (cfv (cv x1) cds) cca) cress) (λ x2 . csb (cfv (cv x2) cbs) (λ x3 . csb (copab (λ x4 x5 . wa (wss (cpr (cv x4) (cv x5)) (cv x3)) (wral (λ x6 . wrex (λ x7 . wf (cfv (cv x7) cuz) (co (cfv (cv x7) (cv x5)) (cv x6) (cfv (cfv (cv x1) cds) cbl)) (cres (cv x4) (cfv (cv x7) cuz))) (λ x7 . cz)) (λ x6 . crp)))) (λ x4 . co (co (cv x2) (cv x4) cqus) (csn (cop (cfv cnx cds) (coprab (λ x5 x6 x7 . wrex (λ x8 . wrex (λ x9 . wa (wa (wceq (cv x5) (cec (cv x8) (cv x4))) (wceq (cv x6) (cec (cv x9) (cv x4)))) (wbr (co (cv x8) (cv x9) (cof (cfv (cv x2) cds))) (cv x7) cli)) (λ x9 . cv x3)) (λ x8 . cv x3))))) csts))))) ⟶ wceq chlb (cmpt (λ x1 . cvv) (λ x1 . csb (ciun (λ x2 . cn) (λ x2 . cxp (csn (cv x2)) (cdm (cfv (cv x2) (cv x1))))) (λ x2 . csb (cint (cab (λ x3 . wa (wer (cv x2) (cv x3)) (wss (cmpt (λ x4 . cv x2) (λ x4 . cop (co (cfv (cv x4) c1st) c1 caddc) (cfv (cfv (cv x4) c2nd) (cfv (cfv (cv x4) c1st) (cv x1))))) (cv x3))))) (λ x3 . cop (cqs (cv x2) (cv x3)) (cmpt (λ x4 . cn) (λ x4 . cmpt (λ x5 . cdm (cfv (cv x4) (cv x1))) (λ x5 . cec (cop (cv x4) (cv x5)) (cv x3)))))))) ⟶ wceq chlim (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x2) chlb) (λ x3 . csb (cfv (cv x3) c1st) (λ x4 . csb (cfv (cv x3) c2nd) (λ x5 . cun (ctp (cop (cfv cnx cbs) (cv x4)) (cop (cfv cnx cplusg) (ciun (λ x6 . cn) (λ x6 . crn (cmpt2 (λ x7 x8 . cdm (cfv (cv x6) (cv x5))) (λ x7 x8 . cdm (cfv (cv x6) (cv x5))) (λ x7 x8 . cop (cop (cfv (cv x7) (cfv (cv x6) (cv x5))) (cfv (cv x8) (cfv (cv x6) (cv x5)))) (cfv (co (cv x7) (cv x8) (cfv (cfv (cv x6) (cv x1)) cplusg)) (cfv (cv x6) (cv x5)))))))) (cop (cfv cnx cmulr) (ciun (λ x6 . cn) (λ x6 . crn (cmpt2 (λ x7 x8 . cdm (cfv (cv x6) (cv x5))) (λ x7 x8 . cdm (cfv (cv x6) (cv x5))) (λ x7 x8 . cop (cop (cfv (cv x7) (cfv (cv x6) (cv x5))) (cfv (cv x8) (cfv (cv x6) (cv x5)))) (cfv (co (cv x7) (cv x8) (cfv (cfv (cv x6) (cv x1)) cmulr)) (cfv (cv x6) (cv x5))))))))) (ctp (cop (cfv cnx ctopn) (crab (λ x6 . wral (λ x7 . wcel (cima (ccnv (cfv (cv x7) (cv x5))) (cv x6)) (cfv (cfv (cv x7) (cv x1)) ctopn)) (λ x7 . cn)) (λ x6 . cpw (cv x4)))) (cop (cfv cnx cds) (ciun (λ x6 . cn) (λ x6 . crn (cmpt2 (λ x7 x8 . cdm (cfv (cv x6) (cfv (cv x6) (cv x5)))) (λ x7 x8 . cdm (cfv (cv x6) (cfv (cv x6) (cv x5)))) (λ x7 x8 . cop (cop (cfv (cv x7) (cfv (cv x6) (cv x5))) (cfv (cv x8) (cfv (cv x6) (cv x5)))) (co (cv x7) (cv x8) (cfv (cfv (cv x6) (cv x1)) cds))))))) (cop (cfv cnx cple) (ciun (λ x6 . cn) (λ x6 . ccom (ccnv (cfv (cv x6) (cv x5))) (ccom (cfv (cfv (cv x6) (cv x1)) cple) (cfv (cv x6) (cv x5)))))))))))) ⟶ wceq cpfl (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . csb (cfv (cv x1) cpl1) (λ x3 . csb (cfv (csn (cv x2)) (cfv (cv x3) crsp)) (λ x4 . csb (cmpt (λ x5 . cfv (cv x1) cbs) (λ x5 . cec (co (cv x5) (cfv (cv x3) cur) (cfv (cv x3) cvsca)) (co (cv x3) (cv x4) cqg))) (λ x5 . cop (csb (co (cv x3) (co (cv x3) (cv x4) cqg) cqus) (λ x6 . co (co (cv x6) (crio (λ x7 . wceq (ccom (cv x7) (cv x5)) (cfv (cv x1) cnm)) (λ x7 . cfv (cv x6) cabv)) ctng) (cop (cfv cnx cple) (csb (cmpt (λ x7 . cfv (cv x6) cbs) (λ x7 . crio (λ x8 . wbr (co (cv x1) (cv x8) cdg1) (co (cv x1) (cv x2) cdg1) clt) (λ x8 . cv x7))) (λ x7 . ccom (ccnv (cv x7)) (ccom (cfv (cv x3) cple) (cv x7))))) csts)) (cv x5)))))) ⟶ wceq csf1 (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cfv (cv x1) cpl1) (λ x3 . cfv (cfv (co c1 (co (cv x1) (cv x3) cdg1) cfz) ccrd) (crdg (cmpt2 (λ x4 x5 . cvv) (λ x4 x5 . cvv) (λ x4 x5 . csb (cfv (cv x4) cmpl) (λ x6 . csb (crab (λ x7 . wa (wbr (cv x7) (ccom (cv x3) (cv x5)) (cfv (cv x6) cdsr)) (wbr c1 (co (cv x4) (cv x7) cdg1) clt)) (λ x7 . cin (cfv (cv x4) cmn1) (cfv (cv x6) cir))) (λ x7 . cif (wo (wceq (ccom (cv x3) (cv x5)) (cfv (cv x6) c0g)) (wceq (cv x7) c0)) (cop (cv x4) (cv x5)) (csb (cfv (cv x7) cglb) (λ x8 . csb (co (cv x4) (cv x8) cpfl) (λ x9 . cop (cfv (cv x9) c1st) (ccom (cv x5) (cfv (cv x9) c2nd))))))))) (cv x2))))) ⟶ wceq csf (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cio (λ x3 . wex (λ x4 . wa (wiso (co c1 (cfv (cv x2) chash) cfz) (cv x2) clt (cfv (cv x1) cplt) (cv x4)) (wceq (cv x3) (cfv (cfv (cv x2) chash) (cseq (cmpt2 (λ x5 x6 . cvv) (λ x5 x6 . cvv) (λ x5 x6 . cfv (cv x6) (co (cv x1) (cv x5) csf1))) (cun (cv x4) (csn (cop cc0 (cop (cv x1) (cres cid (cfv (cv x1) cbs)))))) cc0))))))) ⟶ wceq cpsl (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . co (cin (cpw (cfv (cv x1) cbs)) cfn) cn cmap) (λ x1 x2 . csb (ccom c1st (cseq (cmpt2 (λ x3 x4 . cvv) (λ x3 x4 . cvv) (λ x3 x4 . csb (cfv (cv x3) c1st) (λ x5 . csb (cfv (cv x5) c1st) (λ x6 . csb (co (cv x6) (crn (cmpt (λ x7 . cv x4) (λ x7 . ccom (cv x7) (cfv (cv x3) c2nd)))) csf) (λ x7 . cop (cv x7) (ccom (cfv (cv x3) c2nd) (cfv (cv x7) c2nd))))))) (cun (cv x2) (csn (cop cc0 (cop (cop (cv x1) c0) (cres cid (cfv (cv x1) cbs)))))) cc0)) (λ x3 . co (ccom c1st (co (cv x3) c1 cshi)) (ccom c2nd (cv x3)) chlim))) ⟶ x0) ⟶ x0
Axiom df_zrng__df_gf__df_gfoo__df_eqp__df_rqp__df_qp__df_qpOLD__df_zp__df_qpa__df_cp__df_trpred__df_wsuc__df_wlim__df_frecs__df_no__df_slt__df_bday__df_sle : ∀ x0 : ο . (wceq czr (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (crn (cfv (cv x1) czrh)) citr)) ⟶ wceq cgf (cmpt2 (λ x1 x2 . cprime) (λ x1 x2 . cn) (λ x1 x2 . csb (cfv (cv x1) czn) (λ x3 . cfv (co (cv x3) (csn (csb (cfv (cv x3) cpl1) (λ x4 . csb (cfv (cv x3) cv1) (λ x5 . co (co (co (cv x1) (cv x2) cexp) (cv x5) (cfv (cfv (cv x4) cmgp) cmg)) (cv x5) (cfv (cv x4) csg))))) csf) c1st))) ⟶ wceq cgfo (cmpt (λ x1 . cprime) (λ x1 . csb (cfv (cv x1) czn) (λ x2 . co (cv x2) (cmpt (λ x3 . cn) (λ x3 . csn (csb (cfv (cv x2) cpl1) (λ x4 . csb (cfv (cv x2) cv1) (λ x5 . co (co (co (cv x1) (cv x3) cexp) (cv x5) (cfv (cfv (cv x4) cmgp) cmg)) (cv x5) (cfv (cv x4) csg)))))) cpsl))) ⟶ wceq ceqp (cmpt (λ x1 . cprime) (λ x1 . copab (λ x2 x3 . wa (wss (cpr (cv x2) (cv x3)) (co cz cz cmap)) (wral (λ x4 . wcel (csu (cfv (cneg (cv x4)) cuz) (λ x5 . co (co (cfv (cneg (cv x5)) (cv x2)) (cfv (cneg (cv x5)) (cv x3)) cmin) (co (cv x1) (co (cv x5) (co (cv x4) c1 caddc) caddc) cexp) cdiv)) cz) (λ x4 . cz))))) ⟶ wceq crqp (cmpt (λ x1 . cprime) (λ x1 . cin ceqp (csb (crab (λ x2 . wrex (λ x3 . wss (cima (ccnv (cv x2)) (cdif cz (csn cc0))) (cv x3)) (λ x3 . crn cuz)) (λ x2 . co cz cz cmap)) (λ x2 . cxp (cv x2) (cin (cv x2) (co cz (co cc0 (co (cv x1) c1 cmin) cfz) cmap)))))) ⟶ wceq cqp (cmpt (λ x1 . cprime) (λ x1 . csb (crab (λ x2 . wrex (λ x3 . wss (cima (ccnv (cv x2)) (cdif cz (csn cc0))) (cv x3)) (λ x3 . crn cuz)) (λ x2 . co cz (co cc0 (co (cv x1) c1 cmin) cfz) cmap)) (λ x2 . co (cun (ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . cfv (co (cv x3) (cv x4) (cof caddc)) (cfv (cv x1) crqp)))) (cop (cfv cnx cmulr) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . cfv (cmpt (λ x5 . cz) (λ x5 . csu cz (λ x6 . co (cfv (cv x6) (cv x3)) (cfv (co (cv x5) (cv x6) cmin) (cv x4)) cmul))) (cfv (cv x1) crqp))))) (csn (cop (cfv cnx cple) (copab (λ x3 x4 . wa (wss (cpr (cv x3) (cv x4)) (cv x2)) (wbr (csu cz (λ x5 . co (cfv (cneg (cv x5)) (cv x3)) (co (co (cv x1) c1 caddc) (cneg (cv x5)) cexp) cmul)) (csu cz (λ x5 . co (cfv (cneg (cv x5)) (cv x4)) (co (co (cv x1) c1 caddc) (cneg (cv x5)) cexp) cmul)) clt)))))) (cmpt (λ x3 . cv x2) (λ x3 . cif (wceq (cv x3) (cxp cz (csn cc0))) cc0 (co (cv x1) (cneg (cinf (cima (ccnv (cv x3)) (cdif cz (csn cc0))) cr clt)) cexp))) ctng))) ⟶ wceq cqpOLD (cmpt (λ x1 . cprime) (λ x1 . csb (crab (λ x2 . wrex (λ x3 . wss (cima (ccnv (cv x2)) (cdif cz (csn cc0))) (cv x3)) (λ x3 . crn cuz)) (λ x2 . co cz (co cc0 (co (cv x1) c1 cmin) cfz) cmap)) (λ x2 . co (cun (ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . cfv (co (cv x3) (cv x4) (cof caddc)) (cfv (cv x1) crqp)))) (cop (cfv cnx cmulr) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . cfv (cmpt (λ x5 . cz) (λ x5 . csu cz (λ x6 . co (cfv (cv x6) (cv x3)) (cfv (co (cv x5) (cv x6) cmin) (cv x4)) cmul))) (cfv (cv x1) crqp))))) (csn (cop (cfv cnx cple) (copab (λ x3 x4 . wa (wss (cpr (cv x3) (cv x4)) (cv x2)) (wbr (csu cz (λ x5 . co (cfv (cneg (cv x5)) (cv x3)) (co (co (cv x1) c1 caddc) (cneg (cv x5)) cexp) cmul)) (csu cz (λ x5 . co (cfv (cneg (cv x5)) (cv x4)) (co (co (cv x1) c1 caddc) (cneg (cv x5)) cexp) cmul)) clt)))))) (cmpt (λ x3 . cv x2) (λ x3 . cif (wceq (cv x3) (cxp cz (csn cc0))) cc0 (co (cv x1) (cneg (csup (cima (ccnv (cv x3)) (cdif cz (csn cc0))) cr (ccnv clt))) cexp))) ctng))) ⟶ wceq czp (ccom czr cqp) ⟶ wceq cqpa (cmpt (λ x1 . cprime) (λ x1 . csb (cfv (cv x1) cqp) (λ x2 . co (cv x2) (cmpt (λ x3 . cn) (λ x3 . crab (λ x4 . wa (wbr (co (cv x2) (cv x4) cdg1) (cv x3) cle) (wral (λ x5 . wss (cima (ccnv (cv x5)) (cdif cz (csn cc0))) (co cc0 (cv x3) cfz)) (λ x5 . crn (cfv (cv x4) cco1)))) (λ x4 . cfv (cv x2) cpl1))) cpsl))) ⟶ wceq ccp (ccom ccpms cqpa) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (ctrpred x1 x2 x3) (cuni (crn (cres (crdg (cmpt (λ x4 . cvv) (λ x4 . ciun (λ x5 . cv x4) (λ x5 . cpred x1 x2 (cv x5)))) (cpred x1 x2 x3)) com)))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cwsuc x1 x2 x3) (cinf (cpred x1 (ccnv x2) x3) x1 x2)) ⟶ (∀ x1 x2 : ι → ο . wceq (cwlim x1 x2) (crab (λ x3 . wa (wne (cv x3) (cinf x1 x1 x2)) (wceq (cv x3) (csup (cpred x1 x2 (cv x3)) x1 x2))) (λ x3 . x1))) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (cfrecs x1 x2 x3) (cuni (cab (λ x4 . wex (λ x5 . w3a (wfn (cv x4) (cv x5)) (wa (wss (cv x5) x1) (wral (λ x6 . wss (cpred x1 x2 (cv x6)) (cv x5)) (λ x6 . cv x5))) (wral (λ x6 . wceq (cfv (cv x6) (cv x4)) (co (cv x6) (cres (cv x4) (cpred x1 x2 (cv x6))) x3)) (λ x6 . cv x5))))))) ⟶ wceq csur (cab (λ x1 . wrex (λ x2 . wf (cv x2) (cpr c1o c2o) (cv x1)) (λ x2 . con0))) ⟶ wceq cslt (copab (λ x1 x2 . wa (wa (wcel (cv x1) csur) (wcel (cv x2) csur)) (wrex (λ x3 . wa (wral (λ x4 . wceq (cfv (cv x4) (cv x1)) (cfv (cv x4) (cv x2))) (λ x4 . cv x3)) (wbr (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) (ctp (cop c1o c0) (cop c1o c2o) (cop c0 c2o)))) (λ x3 . con0)))) ⟶ wceq cbday (cmpt (λ x1 . csur) (λ x1 . cdm (cv x1))) ⟶ wceq csle (cdif (cxp csur csur) (ccnv cslt)) ⟶ x0) ⟶ x0
Axiom df_sslt__df_scut__df_made__df_old__df_new__df_left__df_right__df_txp__df_pprod__df_sset__df_trans__df_bigcup__df_fix__df_limits__df_funs__df_singleton__df_singles__df_image : ∀ x0 : ο . (wceq csslt (copab (λ x1 x2 . w3a (wss (cv x1) csur) (wss (cv x2) csur) (wral (λ x3 . wral (λ x4 . wbr (cv x3) (cv x4) cslt) (λ x4 . cv x2)) (λ x3 . cv x1)))) ⟶ wceq cscut (cmpt2 (λ x1 x2 . cpw csur) (λ x1 x2 . cima csslt (csn (cv x1))) (λ x1 x2 . crio (λ x3 . wceq (cfv (cv x3) cbday) (cint (cima cbday (crab (λ x4 . wa (wbr (cv x1) (csn (cv x4)) csslt) (wbr (csn (cv x4)) (cv x2) csslt)) (λ x4 . csur))))) (λ x3 . crab (λ x4 . wa (wbr (cv x1) (csn (cv x4)) csslt) (wbr (csn (cv x4)) (cv x2) csslt)) (λ x4 . csur)))) ⟶ wceq cmade (crecs (cmpt (λ x1 . cvv) (λ x1 . cima cscut (cxp (cpw (cuni (crn (cv x1)))) (cpw (cuni (crn (cv x1)))))))) ⟶ wceq cold (cmpt (λ x1 . con0) (λ x1 . cuni (cima cmade (cv x1)))) ⟶ wceq cnew (cmpt (λ x1 . con0) (λ x1 . cdif (cfv (cv x1) cold) (cfv (cv x1) cmade))) ⟶ wceq cleft (cmpt (λ x1 . csur) (λ x1 . crab (λ x2 . wral (λ x3 . wa (wbr (cv x2) (cv x3) cslt) (wbr (cv x3) (cv x1) cslt) ⟶ wcel (cfv (cv x2) cbday) (cfv (cv x3) cbday)) (λ x3 . csur)) (λ x2 . cfv (cfv (cv x1) cbday) cold))) ⟶ wceq cright (cmpt (λ x1 . csur) (λ x1 . crab (λ x2 . wral (λ x3 . wa (wbr (cv x1) (cv x3) cslt) (wbr (cv x3) (cv x2) cslt) ⟶ wcel (cfv (cv x2) cbday) (cfv (cv x3) cbday)) (λ x3 . csur)) (λ x2 . cfv (cfv (cv x1) cbday) cold))) ⟶ (∀ x1 x2 : ι → ο . wceq (ctxp x1 x2) (cin (ccom (ccnv (cres c1st (cxp cvv cvv))) x1) (ccom (ccnv (cres c2nd (cxp cvv cvv))) x2))) ⟶ (∀ x1 x2 : ι → ο . wceq (cpprod x1 x2) (ctxp (ccom x1 (cres c1st (cxp cvv cvv))) (ccom x2 (cres c2nd (cxp cvv cvv))))) ⟶ wceq csset (cdif (cxp cvv cvv) (crn (ctxp cep (cdif cvv cep)))) ⟶ wceq ctrans (cdif cvv (crn (cdif (ccom cep cep) cep))) ⟶ wceq cbigcup (cdif (cxp cvv cvv) (crn (csymdif (ctxp cvv cep) (ctxp (ccom cep cep) cvv)))) ⟶ (∀ x1 : ι → ο . wceq (cfix x1) (cdm (cin x1 cid))) ⟶ wceq climits (cdif (cin con0 (cfix cbigcup)) (csn c0)) ⟶ wceq cfuns (cdif (cpw (cxp cvv cvv)) (cfix (ccom cep (ccom (ctxp c1st (ccom (cdif cvv cid) c2nd)) (ccnv cep))))) ⟶ wceq csingle (cdif (cxp cvv cvv) (crn (csymdif (ctxp cvv cep) (ctxp cid cvv)))) ⟶ wceq csingles (crn csingle) ⟶ (∀ x1 : ι → ο . wceq (cimage x1) (cdif (cxp cvv cvv) (crn (csymdif (ctxp cvv cep) (ctxp (ccom cep (ccnv x1)) cvv))))) ⟶ x0) ⟶ x0
Axiom df_cart__df_img__df_domain__df_range__df_cup__df_cap__df_restrict__df_succf__df_apply__df_funpart__df_fullfun__df_ub__df_lb__df_altop__df_altxp__df_ofs__df_transport__df_colinear : ∀ x0 : ο . (wceq ccart (cdif (cxp (cxp cvv cvv) cvv) (crn (csymdif (ctxp cvv cep) (ctxp (cpprod cep cep) cvv)))) ⟶ wceq cimg (ccom (cimage (cres (ccom c2nd c1st) (cres c1st (cxp cvv cvv)))) ccart) ⟶ wceq cdomain (cimage (cres c1st (cxp cvv cvv))) ⟶ wceq crange (cimage (cres c2nd (cxp cvv cvv))) ⟶ wceq ccup (cdif (cxp (cxp cvv cvv) cvv) (crn (csymdif (ctxp cvv cep) (ctxp (cun (ccom (ccnv c1st) cep) (ccom (ccnv c2nd) cep)) cvv)))) ⟶ wceq ccap (cdif (cxp (cxp cvv cvv) cvv) (crn (csymdif (ctxp cvv cep) (ctxp (cin (ccom (ccnv c1st) cep) (ccom (ccnv c2nd) cep)) cvv)))) ⟶ wceq crestrict (ccom ccap (ctxp c1st (ccom ccart (ctxp c2nd (ccom crange c1st))))) ⟶ wceq csuccf (ccom ccup (ctxp cid csingle)) ⟶ wceq capply (ccom (ccom cbigcup cbigcup) (ccom (cdif (cxp cvv cvv) (crn (csymdif (ctxp cvv cep) (ctxp (cres cep csingles) cvv)))) (ccom (ccom csingle cimg) (cpprod cid csingle)))) ⟶ (∀ x1 : ι → ο . wceq (cfunpart x1) (cres x1 (cdm (cin (ccom (cimage x1) csingle) (cxp cvv csingles))))) ⟶ (∀ x1 : ι → ο . wceq (cfullfn x1) (cun (cfunpart x1) (cxp (cdif cvv (cdm (cfunpart x1))) (csn c0)))) ⟶ (∀ x1 : ι → ο . wceq (cub x1) (cdif (cxp cvv cvv) (ccom (cdif cvv x1) (ccnv cep)))) ⟶ (∀ x1 : ι → ο . wceq (clb x1) (cub (ccnv x1))) ⟶ (∀ x1 x2 : ι → ο . wceq (caltop x1 x2) (cpr (csn x1) (cpr x1 (csn x2)))) ⟶ (∀ x1 x2 : ι → ο . wceq (caltxp x1 x2) (cab (λ x3 . wrex (λ x4 . wrex (λ x5 . wceq (cv x3) (caltop (cv x4) (cv x5))) (λ x5 . x2)) (λ x4 . x1)))) ⟶ wceq cofs (copab (λ x1 x2 . wrex (λ x3 . wrex (λ x4 . wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . w3a (wceq (cv x1) (cop (cop (cv x4) (cv x5)) (cop (cv x6) (cv x7)))) (wceq (cv x2) (cop (cop (cv x8) (cv x9)) (cop (cv x10) (cv x11)))) (w3a (wa (wbr (cv x5) (cop (cv x4) (cv x6)) cbtwn) (wbr (cv x9) (cop (cv x8) (cv x10)) cbtwn)) (wa (wbr (cop (cv x4) (cv x5)) (cop (cv x8) (cv x9)) ccgr) (wbr (cop (cv x5) (cv x6)) (cop (cv x9) (cv x10)) ccgr)) (wa (wbr (cop (cv x4) (cv x7)) (cop (cv x8) (cv x11)) ccgr) (wbr (cop (cv x5) (cv x7)) (cop (cv x9) (cv x11)) ccgr)))) (λ x11 . cfv (cv x3) cee)) (λ x10 . cfv (cv x3) cee)) (λ x9 . cfv (cv x3) cee)) (λ x8 . cfv (cv x3) cee)) (λ x7 . cfv (cv x3) cee)) (λ x6 . cfv (cv x3) cee)) (λ x5 . cfv (cv x3) cee)) (λ x4 . cfv (cv x3) cee)) (λ x3 . cn))) ⟶ wceq ctransport (coprab (λ x1 x2 x3 . wrex (λ x4 . wa (w3a (wcel (cv x1) (cxp (cfv (cv x4) cee) (cfv (cv x4) cee))) (wcel (cv x2) (cxp (cfv (cv x4) cee) (cfv (cv x4) cee))) (wne (cfv (cv x2) c1st) (cfv (cv x2) c2nd))) (wceq (cv x3) (crio (λ x5 . wa (wbr (cfv (cv x2) c2nd) (cop (cfv (cv x2) c1st) (cv x5)) cbtwn) (wbr (cop (cfv (cv x2) c2nd) (cv x5)) (cv x1) ccgr)) (λ x5 . cfv (cv x4) cee)))) (λ x4 . cn))) ⟶ wceq ccolin (ccnv (coprab (λ x1 x2 x3 . wrex (λ x4 . wa (w3a (wcel (cv x3) (cfv (cv x4) cee)) (wcel (cv x1) (cfv (cv x4) cee)) (wcel (cv x2) (cfv (cv x4) cee))) (w3o (wbr (cv x3) (cop (cv x1) (cv x2)) cbtwn) (wbr (cv x1) (cop (cv x2) (cv x3)) cbtwn) (wbr (cv x2) (cop (cv x3) (cv x1)) cbtwn))) (λ x4 . cn)))) ⟶ x0) ⟶ x0
Axiom df_ifs__df_cgr3__df_fs__df_segle__df_outsideof__df_line2__df_ray__df_lines2__df_fwddif__df_fwddifn__df_hf__df_fne__df_3nand__df_gcdOLD__ax_prv1__ax_prv2__ax_prv3__df_ssb : ∀ x0 : ο . (wceq cifs (copab (λ x1 x2 . wrex (λ x3 . wrex (λ x4 . wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . w3a (wceq (cv x1) (cop (cop (cv x4) (cv x5)) (cop (cv x6) (cv x7)))) (wceq (cv x2) (cop (cop (cv x8) (cv x9)) (cop (cv x10) (cv x11)))) (w3a (wa (wbr (cv x5) (cop (cv x4) (cv x6)) cbtwn) (wbr (cv x9) (cop (cv x8) (cv x10)) cbtwn)) (wa (wbr (cop (cv x4) (cv x6)) (cop (cv x8) (cv x10)) ccgr) (wbr (cop (cv x5) (cv x6)) (cop (cv x9) (cv x10)) ccgr)) (wa (wbr (cop (cv x4) (cv x7)) (cop (cv x8) (cv x11)) ccgr) (wbr (cop (cv x6) (cv x7)) (cop (cv x10) (cv x11)) ccgr)))) (λ x11 . cfv (cv x3) cee)) (λ x10 . cfv (cv x3) cee)) (λ x9 . cfv (cv x3) cee)) (λ x8 . cfv (cv x3) cee)) (λ x7 . cfv (cv x3) cee)) (λ x6 . cfv (cv x3) cee)) (λ x5 . cfv (cv x3) cee)) (λ x4 . cfv (cv x3) cee)) (λ x3 . cn))) ⟶ wceq ccgr3 (copab (λ x1 x2 . wrex (λ x3 . wrex (λ x4 . wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . w3a (wceq (cv x1) (cop (cv x4) (cop (cv x5) (cv x6)))) (wceq (cv x2) (cop (cv x7) (cop (cv x8) (cv x9)))) (w3a (wbr (cop (cv x4) (cv x5)) (cop (cv x7) (cv x8)) ccgr) (wbr (cop (cv x4) (cv x6)) (cop (cv x7) (cv x9)) ccgr) (wbr (cop (cv x5) (cv x6)) (cop (cv x8) (cv x9)) ccgr))) (λ x9 . cfv (cv x3) cee)) (λ x8 . cfv (cv x3) cee)) (λ x7 . cfv (cv x3) cee)) (λ x6 . cfv (cv x3) cee)) (λ x5 . cfv (cv x3) cee)) (λ x4 . cfv (cv x3) cee)) (λ x3 . cn))) ⟶ wceq cfs (copab (λ x1 x2 . wrex (λ x3 . wrex (λ x4 . wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . wrex (λ x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . w3a (wceq (cv x1) (cop (cop (cv x4) (cv x5)) (cop (cv x6) (cv x7)))) (wceq (cv x2) (cop (cop (cv x8) (cv x9)) (cop (cv x10) (cv x11)))) (w3a (wbr (cv x4) (cop (cv x5) (cv x6)) ccolin) (wbr (cop (cv x4) (cop (cv x5) (cv x6))) (cop (cv x8) (cop (cv x9) (cv x10))) ccgr3) (wa (wbr (cop (cv x4) (cv x7)) (cop (cv x8) (cv x11)) ccgr) (wbr (cop (cv x5) (cv x7)) (cop (cv x9) (cv x11)) ccgr)))) (λ x11 . cfv (cv x3) cee)) (λ x10 . cfv (cv x3) cee)) (λ x9 . cfv (cv x3) cee)) (λ x8 . cfv (cv x3) cee)) (λ x7 . cfv (cv x3) cee)) (λ x6 . cfv (cv x3) cee)) (λ x5 . cfv (cv x3) cee)) (λ x4 . cfv (cv x3) cee)) (λ x3 . cn))) ⟶ wceq csegle (copab (λ x1 x2 . wrex (λ x3 . wrex (λ x4 . wrex (λ x5 . wrex (λ x6 . wrex (λ x7 . w3a (wceq (cv x1) (cop (cv x4) (cv x5))) (wceq (cv x2) (cop (cv x6) (cv x7))) (wrex (λ x8 . wa (wbr (cv x8) (cop (cv x6) (cv x7)) cbtwn) (wbr (cop (cv x4) (cv x5)) (cop (cv x6) (cv x8)) ccgr)) (λ x8 . cfv (cv x3) cee))) (λ x7 . cfv (cv x3) cee)) (λ x6 . cfv (cv x3) cee)) (λ x5 . cfv (cv x3) cee)) (λ x4 . cfv (cv x3) cee)) (λ x3 . cn))) ⟶ wceq coutsideof (cdif ccolin cbtwn) ⟶ wceq cline2 (coprab (λ x1 x2 x3 . wrex (λ x4 . wa (w3a (wcel (cv x1) (cfv (cv x4) cee)) (wcel (cv x2) (cfv (cv x4) cee)) (wne (cv x1) (cv x2))) (wceq (cv x3) (cec (cop (cv x1) (cv x2)) (ccnv ccolin)))) (λ x4 . cn))) ⟶ wceq cray (coprab (λ x1 x2 x3 . wrex (λ x4 . wa (w3a (wcel (cv x1) (cfv (cv x4) cee)) (wcel (cv x2) (cfv (cv x4) cee)) (wne (cv x1) (cv x2))) (wceq (cv x3) (crab (λ x5 . wbr (cv x1) (cop (cv x2) (cv x5)) coutsideof) (λ x5 . cfv (cv x4) cee)))) (λ x4 . cn))) ⟶ wceq clines2 (crn cline2) ⟶ wceq cfwddif (cmpt (λ x1 . co cc cc cpm) (λ x1 . cmpt (λ x2 . crab (λ x3 . wcel (co (cv x3) c1 caddc) (cdm (cv x1))) (λ x3 . cdm (cv x1))) (λ x2 . co (cfv (co (cv x2) c1 caddc) (cv x1)) (cfv (cv x2) (cv x1)) cmin))) ⟶ wceq cfwddifn (cmpt2 (λ x1 x2 . cn0) (λ x1 x2 . co cc cc cpm) (λ x1 x2 . cmpt (λ x3 . crab (λ x4 . wral (λ x5 . wcel (co (cv x4) (cv x5) caddc) (cdm (cv x2))) (λ x5 . co cc0 (cv x1) cfz)) (λ x4 . cc)) (λ x3 . csu (co cc0 (cv x1) cfz) (λ x4 . co (co (cv x1) (cv x4) cbc) (co (co (cneg c1) (co (cv x1) (cv x4) cmin) cexp) (cfv (co (cv x3) (cv x4) caddc) (cv x2)) cmul) cmul)))) ⟶ wceq chf (cuni (cima cr1 com)) ⟶ wceq cfne (copab (λ x1 x2 . wa (wceq (cuni (cv x1)) (cuni (cv x2))) (wral (λ x3 . wss (cv x3) (cuni (cin (cv x2) (cpw (cv x3))))) (λ x3 . cv x1)))) ⟶ (∀ x1 x2 x3 : ο . wb (w3nand x1 x2 x3) (x1 ⟶ x2 ⟶ wn x3)) ⟶ (∀ x1 x2 : ι → ο . wceq (cgcdOLD x1 x2) (csup (crab (λ x3 . wa (wcel (co x1 (cv x3) cdiv) cn) (wcel (co x2 (cv x3) cdiv) cn)) (λ x3 . cn)) cn clt)) ⟶ (∀ x1 : ο . x1 ⟶ cprvb x1) ⟶ (∀ x1 x2 : ο . cprvb (x1 ⟶ x2) ⟶ cprvb x1 ⟶ cprvb x2) ⟶ (∀ x1 : ο . cprvb x1 ⟶ cprvb (cprvb x1)) ⟶ (∀ x1 : ι → ο . ∀ x2 . wb (wssb x1 x2) (∀ x3 . wceq (cv x3) (cv x2) ⟶ ∀ x4 . wceq (cv x4) (cv x3) ⟶ x1 x4)) ⟶ x0) ⟶ x0
Axiom df_ssb_b__df_bj_rnf__df_bj_sngl__df_bj_tag__df_bj_proj__df_bj_1upl__df_bj_pr1__df_bj_2upl__df_bj_pr2__df_elwise__df_bj_moore__df_bj_mpt3__df_bj_sethom__df_bj_tophom__df_bj_mgmhom__df_bj_topmgmhom__df_bj_cur__df_bj_unc : ∀ x0 : ο . ((∀ x1 : ι → ο . ∀ x2 . wb (wssb x1 x2) (∀ x3 . wceq (cv x3) (cv x2) ⟶ ∀ x4 . wceq (cv x4) (cv x3) ⟶ x1 x4)) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (wrnf x1 x2) (wrex x1 x2 ⟶ wral x1 x2)) ⟶ (∀ x1 : ι → ο . wceq (bj_csngl x1) (cab (λ x2 . wrex (λ x3 . wceq (cv x2) (csn (cv x3))) (λ x3 . x1)))) ⟶ (∀ x1 : ι → ο . wceq (bj_ctag x1) (cun (bj_csngl x1) (csn c0))) ⟶ (∀ x1 x2 : ι → ο . wceq (bj_cproj x1 x2) (cab (λ x3 . wcel (csn (cv x3)) (cima x2 (csn x1))))) ⟶ (∀ x1 : ι → ο . wceq (bj_c1upl x1) (cxp (csn c0) (bj_ctag x1))) ⟶ (∀ x1 : ι → ο . wceq (bj_cpr1 x1) (bj_cproj c0 x1)) ⟶ (∀ x1 x2 : ι → ο . wceq (bj_c2uple x1 x2) (cun (bj_c1upl x1) (cxp (csn c1o) (bj_ctag x2)))) ⟶ (∀ x1 : ι → ο . wceq (bj_cpr2 x1) (bj_cproj c1o x1)) ⟶ wceq celwise (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cvv) (λ x2 x3 . cvv) (λ x2 x3 . cab (λ x4 . wrex (λ x5 . wrex (λ x6 . wceq (cv x4) (co (cv x5) (cv x6) (cv x1))) (λ x6 . cv x3)) (λ x5 . cv x2))))) ⟶ wceq cmoore (cab (λ x1 . wral (λ x2 . wcel (cin (cuni (cv x1)) (cint (cv x2))) (cv x1)) (λ x2 . cpw (cv x1)))) ⟶ (∀ x1 x2 x3 x4 : ι → ι → ι → ι → ο . ∀ x5 x6 . wceq (cmpt3 x1 x2 x3 x4) (copab (λ x7 x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . wa (wceq (cv x7) (cotp (cv x9) (cv x10) (cv x11))) (wceq (cv x8) (x4 x9 x10 x11))) (x3 x9 x10)) (λ x10 . x2 x9 x10 x6)) (λ x9 . x1 x9 x5 x6)))) ⟶ wceq csethom (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cab (λ x3 . wf (cv x1) (cv x2) (cv x3)))) ⟶ wceq ctophom (cmpt2 (λ x1 x2 . ctps) (λ x1 x2 . ctps) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wcel (cima (ccnv (cv x3)) (cv x4)) (cfv (cv x1) ctopn)) (λ x4 . cfv (cv x2) ctopn)) (λ x3 . co (cfv (cv x1) cbs) (cfv (cv x2) cbs) csethom))) ⟶ wceq cmgmhom (cmpt2 (λ x1 x2 . cmgm) (λ x1 x2 . cmgm) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wceq (cfv (co (cv x4) (cv x5) (cfv (cv x1) cplusg)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) cplusg))) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . co (cfv (cv x1) cbs) (cfv (cv x2) cbs) csethom))) ⟶ wceq ctopmgmhom (cmpt2 (λ x1 x2 . ctmd) (λ x1 x2 . ctmd) (λ x1 x2 . cin (co (cv x1) (cv x2) ctophom) (co (cv x1) (cv x2) cmgmhom))) ⟶ wceq ccur_ (cmpt3 (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cmpt (λ x4 . co (cxp (cv x1) (cv x2)) (cv x3) csethom) (λ x4 . cmpt (λ x5 . cv x1) (λ x5 . cmpt (λ x6 . cv x2) (λ x6 . cfv (cop (cv x5) (cv x6)) (cv x4)))))) ⟶ wceq cunc_ (cmpt3 (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cvv) (λ x1 x2 x3 . cmpt (λ x4 . co (cv x1) (co (cv x2) (cv x3) csethom) csethom) (λ x4 . cmpt2 (λ x5 x6 . cv x1) (λ x5 x6 . cv x2) (λ x5 x6 . cfv (cv x6) (cfv (cv x5) (cv x4)))))) ⟶ x0) ⟶ x0
Axiom df_strset__df_bj_diag__df_bj_inftyexpi__df_bj_ccinfty__df_bj_ccbar__df_bj_pinfty__df_bj_minfty__df_bj_rrbar__df_bj_infty__df_bj_cchat__df_bj_rrhat__df_bj_addc__df_bj_oppc__df_bj_prcpal__df_bj_arg__df_bj_mulc__df_bj_invc__df_bj_finsum : ∀ x0 : ο . ((∀ x1 x2 x3 : ι → ο . wceq (cstrset x1 x2 x3) (cun (cres x3 (cdif cvv (csn (cfv cnx x1)))) (csn (cop (cfv cnx x1) x2)))) ⟶ wceq cdiag2 (cmpt (λ x1 . cvv) (λ x1 . cin cid (cxp (cv x1) (cv x1)))) ⟶ wceq cinftyexpi (cmpt (λ x1 . co (cneg cpi) cpi cioc) (λ x1 . cop (cv x1) cc)) ⟶ wceq cccinfty (crn cinftyexpi) ⟶ wceq cccbar (cun cc cccinfty) ⟶ wceq cpinfty (cfv cc0 cinftyexpi) ⟶ wceq cminfty (cfv cpi cinftyexpi) ⟶ wceq crrbar (cun cr (cpr cminfty cpinfty)) ⟶ wceq cinfty (cpw (cuni cc)) ⟶ wceq ccchat (cun cc (csn cinfty)) ⟶ wceq crrhat (cun cr (csn cinfty)) ⟶ wceq caddcc (cmpt (λ x1 . cun (cun (cxp cc cccbar) (cxp cccbar cc)) (cun (cxp ccchat ccchat) (cfv cccinfty cdiag2))) (λ x1 . cif (wo (wceq (cfv (cv x1) c1st) cinfty) (wceq (cfv (cv x1) c2nd) cinfty)) cinfty (cif (wcel (cfv (cv x1) c1st) cc) (cif (wcel (cfv (cv x1) c2nd) cc) (co (cfv (cv x1) c1st) (cfv (cv x1) c2nd) caddc) (cfv (cv x1) c2nd)) (cfv (cv x1) c1st)))) ⟶ wceq coppcc (cmpt (λ x1 . cun cccbar ccchat) (λ x1 . cif (wceq (cv x1) cinfty) cinfty (cif (wcel (cv x1) cc) (cneg (cv x1)) (cfv (cif (wbr cc0 (cfv (cv x1) c1st) clt) (co (cfv (cv x1) c1st) cpi cmin) (co (cfv (cv x1) c1st) cpi caddc)) cinftyexpi)))) ⟶ wceq cprcpal (cmpt (λ x1 . cr) (λ x1 . co (co (cv x1) (co c2 cpi cmul) cmo) (cif (wbr (co (cv x1) (co c2 cpi cmul) cmo) cpi cle) cc0 (co c2 cpi cmul)) cmin)) ⟶ wceq carg (cmpt (λ x1 . cdif cccbar (csn cc0)) (λ x1 . cif (wcel (cv x1) cc) (cfv (cfv (cv x1) clog) cim) (cfv (cv x1) c1st))) ⟶ wceq cmulc (cmpt (λ x1 . cun (cxp cccbar cccbar) (cxp ccchat ccchat)) (λ x1 . cif (wo (wceq (cfv (cv x1) c1st) cc0) (wceq (cfv (cv x1) c2nd) cc0)) cc0 (cif (wo (wceq (cfv (cv x1) c1st) cinfty) (wceq (cfv (cv x1) c2nd) cinfty)) cinfty (cif (wcel (cv x1) (cxp cc cc)) (co (cfv (cv x1) c1st) (cfv (cv x1) c2nd) cmul) (cfv (cfv (co (cfv (cfv (cv x1) c1st) carg) (cfv (cfv (cv x1) c2nd) carg) caddc) cprcpal) cinftyexpi))))) ⟶ wceq cinvc (cmpt (λ x1 . cun cccbar ccchat) (λ x1 . cif (wceq (cv x1) cc0) cinfty (cif (wcel (cv x1) cc) (co c1 (cv x1) cdiv) cc0))) ⟶ wceq cfinsum (cmpt (λ x1 . copab (λ x2 x3 . wa (wcel (cv x2) ccmn) (wrex (λ x4 . wf (cv x4) (cfv (cv x2) cbs) (cv x3)) (λ x4 . cfn)))) (λ x1 . cio (λ x2 . wrex (λ x3 . wex (λ x4 . wa (wf1o (co c1 (cv x3) cfz) (cdm (cfv (cv x1) c2nd)) (cv x4)) (wceq (cv x2) (cfv (cv x3) (cseq (cfv (cfv (cv x1) c1st) cplusg) (cmpt (λ x5 . cn) (λ x5 . cfv (cfv (cv x5) (cv x4)) (cfv (cv x1) c2nd))) c1))))) (λ x3 . cn0)))) ⟶ x0) ⟶ x0
Axiom df_bj_rrvec__df_tau__df_finxp__ax_luk1__ax_luk2__ax_luk3__ax_wl_13v__ax_wl_11v__ax_wl_8cl__df_wl_clelv2__df_totbnd__df_bnd__df_ismty__df_rrn__df_ass__df_exid__df_mgmOLD__df_sgrOLD : ∀ x0 : ο . (wceq crrvec (crab (λ x1 . wceq (cfv (cv x1) csca) crefld) (λ x1 . clvec)) ⟶ wceq ctau (cinf (cin crp (cima (ccnv ccos) (csn c1))) cr clt) ⟶ (∀ x1 x2 : ι → ο . wceq (cfinxp x1 x2) (cab (λ x3 . wa (wcel x2 com) (wceq c0 (cfv x2 (crdg (cmpt2 (λ x4 x5 . com) (λ x4 x5 . cvv) (λ x4 x5 . cif (wa (wceq (cv x4) c1o) (wcel (cv x5) x1)) c0 (cif (wcel (cv x5) (cxp cvv x1)) (cop (cuni (cv x4)) (cfv (cv x5) c1st)) (cop (cv x4) (cv x5))))) (cop x2 (cv x3)))))))) ⟶ (∀ x1 x2 x3 : ο . (x1 ⟶ x2) ⟶ (x2 ⟶ x3) ⟶ x1 ⟶ x3) ⟶ (∀ x1 : ο . (wn x1 ⟶ x1) ⟶ x1) ⟶ (∀ x1 x2 : ο . x1 ⟶ wn x1 ⟶ x2) ⟶ (∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x1)) ⟶ wceq (cv x1) (cv x2) ⟶ ∀ x3 . wceq (cv x1) (cv x2)) ⟶ (∀ x1 : ι → ι → ο . (∀ x2 x3 . x1 x2 x3) ⟶ ∀ x2 x3 . x1 x3 x2) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 . wceq (cv x2) (cv x3) ⟶ wcel_wl (λ x4 . x1) ⟶ wcel_wl (λ x4 . x1)) ⟶ (∀ x1 : ι → ι → ο . ∀ x2 . wb (wcel2_wl x1) (∀ x3 . wceq (cv x3) (cv x2) ⟶ wcel_wl (λ x4 . x1 x2))) ⟶ wceq ctotbnd (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wa (wceq (cuni (cv x4)) (cv x1)) (wral (λ x5 . wrex (λ x6 . wceq (cv x5) (co (cv x6) (cv x3) (cfv (cv x2) cbl))) (λ x6 . cv x1)) (λ x5 . cv x4))) (λ x4 . cfn)) (λ x3 . crp)) (λ x2 . cfv (cv x1) cme))) ⟶ wceq cbnd (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wceq (cv x1) (co (cv x3) (cv x4) (cfv (cv x2) cbl))) (λ x4 . crp)) (λ x3 . cv x1)) (λ x2 . cfv (cv x1) cme))) ⟶ wceq cismty (cmpt2 (λ x1 x2 . cuni (crn cxmt)) (λ x1 x2 . cuni (crn cxmt)) (λ x1 x2 . cab (λ x3 . wa (wf1o (cdm (cdm (cv x1))) (cdm (cdm (cv x2))) (cv x3)) (wral (λ x4 . wral (λ x5 . wceq (co (cv x4) (cv x5) (cv x1)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cv x2))) (λ x5 . cdm (cdm (cv x1)))) (λ x4 . cdm (cdm (cv x1))))))) ⟶ wceq crrn (cmpt (λ x1 . cfn) (λ x1 . cmpt2 (λ x2 x3 . co cr (cv x1) cmap) (λ x2 x3 . co cr (cv x1) cmap) (λ x2 x3 . cfv (csu (cv x1) (λ x4 . co (co (cfv (cv x4) (cv x2)) (cfv (cv x4) (cv x3)) cmin) c2 cexp)) csqrt))) ⟶ wceq cass (cab (λ x1 . wral (λ x2 . wral (λ x3 . wral (λ x4 . wceq (co (co (cv x2) (cv x3) (cv x1)) (cv x4) (cv x1)) (co (cv x2) (co (cv x3) (cv x4) (cv x1)) (cv x1))) (λ x4 . cdm (cdm (cv x1)))) (λ x3 . cdm (cdm (cv x1)))) (λ x2 . cdm (cdm (cv x1))))) ⟶ wceq cexid (cab (λ x1 . wrex (λ x2 . wral (λ x3 . wa (wceq (co (cv x2) (cv x3) (cv x1)) (cv x3)) (wceq (co (cv x3) (cv x2) (cv x1)) (cv x3))) (λ x3 . cdm (cdm (cv x1)))) (λ x2 . cdm (cdm (cv x1))))) ⟶ wceq cmagm (cab (λ x1 . wex (λ x2 . wf (cxp (cv x2) (cv x2)) (cv x2) (cv x1)))) ⟶ wceq csem (cin cmagm cass) ⟶ x0) ⟶ x0
Axiom df_mndo__df_ghomOLD__df_rngo__df_drngo__df_rngohom__df_rngoiso__df_risc__df_com2__df_fld__df_crngo__df_idl__df_pridl__df_maxidl__df_prrngo__df_dmn__df_igen__df_xrn__df_coss : ∀ x0 : ο . (wceq cmndo (cin csem cexid) ⟶ wceq cghomOLD (cmpt2 (λ x1 x2 . cgr) (λ x1 x2 . cgr) (λ x1 x2 . cab (λ x3 . wa (wf (crn (cv x1)) (crn (cv x2)) (cv x3)) (wral (λ x4 . wral (λ x5 . wceq (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cv x2)) (cfv (co (cv x4) (cv x5) (cv x1)) (cv x3))) (λ x5 . crn (cv x1))) (λ x4 . crn (cv x1)))))) ⟶ wceq crngo (copab (λ x1 x2 . wa (wa (wcel (cv x1) cablo) (wf (cxp (crn (cv x1)) (crn (cv x1))) (crn (cv x1)) (cv x2))) (wa (wral (λ x3 . wral (λ x4 . wral (λ x5 . w3a (wceq (co (co (cv x3) (cv x4) (cv x2)) (cv x5) (cv x2)) (co (cv x3) (co (cv x4) (cv x5) (cv x2)) (cv x2))) (wceq (co (cv x3) (co (cv x4) (cv x5) (cv x1)) (cv x2)) (co (co (cv x3) (cv x4) (cv x2)) (co (cv x3) (cv x5) (cv x2)) (cv x1))) (wceq (co (co (cv x3) (cv x4) (cv x1)) (cv x5) (cv x2)) (co (co (cv x3) (cv x5) (cv x2)) (co (cv x4) (cv x5) (cv x2)) (cv x1)))) (λ x5 . crn (cv x1))) (λ x4 . crn (cv x1))) (λ x3 . crn (cv x1))) (wrex (λ x3 . wral (λ x4 . wa (wceq (co (cv x3) (cv x4) (cv x2)) (cv x4)) (wceq (co (cv x4) (cv x3) (cv x2)) (cv x4))) (λ x4 . crn (cv x1))) (λ x3 . crn (cv x1)))))) ⟶ wceq cdrng (copab (λ x1 x2 . wa (wcel (cop (cv x1) (cv x2)) crngo) (wcel (cres (cv x2) (cxp (cdif (crn (cv x1)) (csn (cfv (cv x1) cgi))) (cdif (crn (cv x1)) (csn (cfv (cv x1) cgi))))) cgr))) ⟶ wceq crnghom (cmpt2 (λ x1 x2 . crngo) (λ x1 x2 . crngo) (λ x1 x2 . crab (λ x3 . wa (wceq (cfv (cfv (cfv (cv x1) c2nd) cgi) (cv x3)) (cfv (cfv (cv x2) c2nd) cgi)) (wral (λ x4 . wral (λ x5 . wa (wceq (cfv (co (cv x4) (cv x5) (cfv (cv x1) c1st)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) c1st))) (wceq (cfv (co (cv x4) (cv x5) (cfv (cv x1) c2nd)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) c2nd)))) (λ x5 . crn (cfv (cv x1) c1st))) (λ x4 . crn (cfv (cv x1) c1st)))) (λ x3 . co (crn (cfv (cv x2) c1st)) (crn (cfv (cv x1) c1st)) cmap))) ⟶ wceq crngiso (cmpt2 (λ x1 x2 . crngo) (λ x1 x2 . crngo) (λ x1 x2 . crab (λ x3 . wf1o (crn (cfv (cv x1) c1st)) (crn (cfv (cv x2) c1st)) (cv x3)) (λ x3 . co (cv x1) (cv x2) crnghom))) ⟶ wceq crisc (copab (λ x1 x2 . wa (wa (wcel (cv x1) crngo) (wcel (cv x2) crngo)) (wex (λ x3 . wcel (cv x3) (co (cv x1) (cv x2) crngiso))))) ⟶ wceq ccm2 (copab (λ x1 x2 . wral (λ x3 . wral (λ x4 . wceq (co (cv x3) (cv x4) (cv x2)) (co (cv x4) (cv x3) (cv x2))) (λ x4 . crn (cv x1))) (λ x3 . crn (cv x1)))) ⟶ wceq cfld (cin cdrng ccm2) ⟶ wceq ccring (cin crngo ccm2) ⟶ wceq cidl (cmpt (λ x1 . crngo) (λ x1 . crab (λ x2 . wa (wcel (cfv (cfv (cv x1) c1st) cgi) (cv x2)) (wral (λ x3 . wa (wral (λ x4 . wcel (co (cv x3) (cv x4) (cfv (cv x1) c1st)) (cv x2)) (λ x4 . cv x2)) (wral (λ x4 . wa (wcel (co (cv x4) (cv x3) (cfv (cv x1) c2nd)) (cv x2)) (wcel (co (cv x3) (cv x4) (cfv (cv x1) c2nd)) (cv x2))) (λ x4 . crn (cfv (cv x1) c1st)))) (λ x3 . cv x2))) (λ x2 . cpw (crn (cfv (cv x1) c1st))))) ⟶ wceq cpridl (cmpt (λ x1 . crngo) (λ x1 . crab (λ x2 . wa (wne (cv x2) (crn (cfv (cv x1) c1st))) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wcel (co (cv x5) (cv x6) (cfv (cv x1) c2nd)) (cv x2)) (λ x6 . cv x4)) (λ x5 . cv x3) ⟶ wo (wss (cv x3) (cv x2)) (wss (cv x4) (cv x2))) (λ x4 . cfv (cv x1) cidl)) (λ x3 . cfv (cv x1) cidl))) (λ x2 . cfv (cv x1) cidl))) ⟶ wceq cmaxidl (cmpt (λ x1 . crngo) (λ x1 . crab (λ x2 . wa (wne (cv x2) (crn (cfv (cv x1) c1st))) (wral (λ x3 . wss (cv x2) (cv x3) ⟶ wo (wceq (cv x3) (cv x2)) (wceq (cv x3) (crn (cfv (cv x1) c1st)))) (λ x3 . cfv (cv x1) cidl))) (λ x2 . cfv (cv x1) cidl))) ⟶ wceq cprrng (crab (λ x1 . wcel (csn (cfv (cfv (cv x1) c1st) cgi)) (cfv (cv x1) cpridl)) (λ x1 . crngo)) ⟶ wceq cdmn (cin cprrng ccm2) ⟶ wceq cigen (cmpt2 (λ x1 x2 . crngo) (λ x1 x2 . cpw (crn (cfv (cv x1) c1st))) (λ x1 x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) cidl)))) ⟶ (∀ x1 x2 : ι → ο . wceq (cxrn x1 x2) (cin (ccom (ccnv (cres c1st (cxp cvv cvv))) x1) (ccom (ccnv (cres c2nd (cxp cvv cvv))) x2))) ⟶ (∀ x1 : ι → ο . wceq (ccoss x1) (copab (λ x2 x3 . wex (λ x4 . wa (wbr (cv x4) (cv x2) x1) (wbr (cv x4) (cv x3) x1))))) ⟶ x0) ⟶ x0
Axiom df_coels__df_rels__df_ssr__df_refs__df_refrels__df_refrel__df_cnvrefs__df_cnvrefrels__df_cnvrefrel__df_syms__df_symrels__df_symrel__df_prt__ax_c5__ax_c4__ax_c7__ax_c10__ax_c10_b : ∀ x0 : ο . ((∀ x1 : ι → ο . wceq (ccoels x1) (ccoss (cres (ccnv cep) x1))) ⟶ wceq crels (cpw (cxp cvv cvv)) ⟶ wceq cssr (copab (λ x1 x2 . wss (cv x1) (cv x2))) ⟶ wceq crefs (cab (λ x1 . wbr (cin cid (cxp (cdm (cv x1)) (crn (cv x1)))) (cin (cv x1) (cxp (cdm (cv x1)) (crn (cv x1)))) cssr)) ⟶ wceq crefrels (cin crefs crels) ⟶ (∀ x1 : ι → ο . wb (wrefrel x1) (wa (wss (cin cid (cxp (cdm x1) (crn x1))) (cin x1 (cxp (cdm x1) (crn x1)))) (wrel x1))) ⟶ wceq ccnvrefs (cab (λ x1 . wbr (cin cid (cxp (cdm (cv x1)) (crn (cv x1)))) (cin (cv x1) (cxp (cdm (cv x1)) (crn (cv x1)))) (ccnv cssr))) ⟶ wceq ccnvrefrels (cin ccnvrefs crels) ⟶ (∀ x1 : ι → ο . wb (wcnvrefrel x1) (wa (wss (cin x1 (cxp (cdm x1) (crn x1))) (cin cid (cxp (cdm x1) (crn x1)))) (wrel x1))) ⟶ wceq csyms (cab (λ x1 . wbr (ccnv (cin (cv x1) (cxp (cdm (cv x1)) (crn (cv x1))))) (cin (cv x1) (cxp (cdm (cv x1)) (crn (cv x1)))) cssr)) ⟶ wceq csymrels (cin csyms crels) ⟶ (∀ x1 : ι → ο . wb (wsymrel x1) (wa (wss (ccnv (cin x1 (cxp (cdm x1) (crn x1)))) (cin x1 (cxp (cdm x1) (crn x1)))) (wrel x1))) ⟶ (∀ x1 : ι → ο . wb (wprt x1) (wral (λ x2 . wral (λ x3 . wo (wceq (cv x2) (cv x3)) (wceq (cin (cv x2) (cv x3)) c0)) (λ x3 . x1)) (λ x2 . x1))) ⟶ (∀ x1 : ι → ο . ∀ x2 . (∀ x3 . x1 x3) ⟶ x1 x2) ⟶ (∀ x1 x2 : ι → ο . (∀ x3 . (∀ x4 . x1 x4) ⟶ x2 x3) ⟶ (∀ x3 . x1 x3) ⟶ ∀ x3 . x2 x3) ⟶ (∀ x1 : ι → ο . ∀ x2 . wn (∀ x3 . wn (∀ x4 . x1 x4)) ⟶ x1 x2) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 . (∀ x4 . wceq (cv x4) (cv x2) ⟶ ∀ x5 . x1 x5) ⟶ x1 x3) ⟶ (∀ x1 : ι → ο . ∀ x2 . (∀ x3 . wceq (cv x3) (cv x3) ⟶ ∀ x4 . x1 x4) ⟶ x1 x2) ⟶ x0) ⟶ x0
Axiom ax_c11__ax_c11_b__ax_c11n__ax_c15__ax_c9__ax_c9_b__ax_c9_b1__ax_c9_b2__ax_c9_b3__ax_c14__ax_c16__ax_riotaBAD__df_lsatoms__df_lshyp__df_lcv__df_lfl__df_lkr__df_ldual : ∀ x0 : ο . ((∀ x1 : ι → ι → ο . ∀ x2 x3 . (∀ x4 . wceq (cv x4) (cv x3)) ⟶ (∀ x4 . x1 x4 x3) ⟶ ∀ x4 . x1 x2 x4) ⟶ (∀ x1 : ι → ο . (∀ x2 . wceq (cv x2) (cv x2)) ⟶ (∀ x2 . x1 x2) ⟶ ∀ x2 . x1 x2) ⟶ (∀ x1 x2 . (∀ x3 . wceq (cv x3) (cv x2)) ⟶ ∀ x3 . wceq (cv x3) (cv x1)) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 . wn (∀ x4 . wceq (cv x4) (cv x2)) ⟶ wceq (cv x3) (cv x2) ⟶ x1 x3 ⟶ ∀ x4 . wceq (cv x4) (cv x2) ⟶ x1 x4) ⟶ (∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x1)) ⟶ wn (∀ x3 . wceq (cv x3) (cv x2)) ⟶ wceq (cv x1) (cv x2) ⟶ ∀ x3 . wceq (cv x1) (cv x2)) ⟶ (∀ x1 . wn (∀ x2 . wceq (cv x2) (cv x2)) ⟶ wn (∀ x2 . wceq (cv x2) (cv x2)) ⟶ wceq (cv x1) (cv x1) ⟶ ∀ x2 . wceq (cv x2) (cv x2)) ⟶ (∀ x1 . wn (∀ x2 . wceq (cv x2) (cv x1)) ⟶ wn (∀ x2 . wceq (cv x2) (cv x1)) ⟶ wceq (cv x1) (cv x1) ⟶ ∀ x2 . wceq (cv x1) (cv x1)) ⟶ (∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x3)) ⟶ wn (∀ x3 . wceq (cv x3) (cv x1)) ⟶ wceq (cv x2) (cv x1) ⟶ ∀ x3 . wceq (cv x3) (cv x1)) ⟶ (∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x1)) ⟶ wn (∀ x3 . wceq (cv x3) (cv x3)) ⟶ wceq (cv x1) (cv x2) ⟶ ∀ x3 . wceq (cv x1) (cv x3)) ⟶ (∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x1)) ⟶ wn (∀ x3 . wceq (cv x3) (cv x2)) ⟶ wcel (cv x1) (cv x2) ⟶ ∀ x3 . wcel (cv x1) (cv x2)) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 . (∀ x4 . wceq (cv x4) (cv x2)) ⟶ x1 x3 ⟶ ∀ x4 . x1 x4) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wceq (crio x1 x2) (cif (wreu x1 x2) (cio (λ x3 . wa (wcel (cv x3) (x2 x3)) (x1 x3))) (cfv (cab (λ x3 . wcel (cv x3) (x2 x3))) cund))) ⟶ wceq clsa (cmpt (λ x1 . cvv) (λ x1 . crn (cmpt (λ x2 . cdif (cfv (cv x1) cbs) (csn (cfv (cv x1) c0g))) (λ x2 . cfv (csn (cv x2)) (cfv (cv x1) clspn))))) ⟶ wceq clsh (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wne (cv x2) (cfv (cv x1) cbs)) (wrex (λ x3 . wceq (cfv (cun (cv x2) (csn (cv x3))) (cfv (cv x1) clspn)) (cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) cbs))) (λ x2 . cfv (cv x1) clss))) ⟶ wceq clcv (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . wa (wa (wcel (cv x2) (cfv (cv x1) clss)) (wcel (cv x3) (cfv (cv x1) clss))) (wa (wpss (cv x2) (cv x3)) (wn (wrex (λ x4 . wa (wpss (cv x2) (cv x4)) (wpss (cv x4) (cv x3))) (λ x4 . cfv (cv x1) clss))))))) ⟶ wceq clfn (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wral (λ x4 . wral (λ x5 . wceq (cfv (co (co (cv x3) (cv x4) (cfv (cv x1) cvsca)) (cv x5) (cfv (cv x1) cplusg)) (cv x2)) (co (co (cv x3) (cfv (cv x4) (cv x2)) (cfv (cfv (cv x1) csca) cmulr)) (cfv (cv x5) (cv x2)) (cfv (cfv (cv x1) csca) cplusg))) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cfv (cv x1) csca) cbs)) (λ x2 . co (cfv (cfv (cv x1) csca) cbs) (cfv (cv x1) cbs) cmap))) ⟶ wceq clk (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clfn) (λ x2 . cima (ccnv (cv x2)) (csn (cfv (cfv (cv x1) csca) c0g))))) ⟶ wceq cld (cmpt (λ x1 . cvv) (λ x1 . cun (ctp (cop (cfv cnx cbs) (cfv (cv x1) clfn)) (cop (cfv cnx cplusg) (cres (cof (cfv (cfv (cv x1) csca) cplusg)) (cxp (cfv (cv x1) clfn) (cfv (cv x1) clfn)))) (cop (cfv cnx csca) (cfv (cfv (cv x1) csca) coppr))) (csn (cop (cfv cnx cvsca) (cmpt2 (λ x2 x3 . cfv (cfv (cv x1) csca) cbs) (λ x2 x3 . cfv (cv x1) clfn) (λ x2 x3 . co (cv x3) (cxp (cfv (cv x1) cbs) (csn (cv x2))) (cof (cfv (cfv (cv x1) csca) cmulr)))))))) ⟶ x0) ⟶ x0
Axiom df_oposet__df_cmtN__df_ol__df_oml__df_covers__df_ats__df_atl__df_cvlat__df_hlat__df_llines__df_lplanes__df_lvols__df_lines__df_pointsN__df_psubsp__df_pmap__df_padd__df_pclN : ∀ x0 : ο . (wceq cops (crab (λ x1 . wa (wa (wcel (cfv (cv x1) cbs) (cdm (cfv (cv x1) club))) (wcel (cfv (cv x1) cbs) (cdm (cfv (cv x1) cglb)))) (wex (λ x2 . wa (wceq (cv x2) (cfv (cv x1) coc)) (wral (λ x3 . wral (λ x4 . w3a (w3a (wcel (cfv (cv x3) (cv x2)) (cfv (cv x1) cbs)) (wceq (cfv (cfv (cv x3) (cv x2)) (cv x2)) (cv x3)) (wbr (cv x3) (cv x4) (cfv (cv x1) cple) ⟶ wbr (cfv (cv x4) (cv x2)) (cfv (cv x3) (cv x2)) (cfv (cv x1) cple))) (wceq (co (cv x3) (cfv (cv x3) (cv x2)) (cfv (cv x1) cjn)) (cfv (cv x1) cp1)) (wceq (co (cv x3) (cfv (cv x3) (cv x2)) (cfv (cv x1) cmee)) (cfv (cv x1) cp0))) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) cbs))))) (λ x1 . cpo)) ⟶ wceq ccmtN (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . w3a (wcel (cv x2) (cfv (cv x1) cbs)) (wcel (cv x3) (cfv (cv x1) cbs)) (wceq (cv x2) (co (co (cv x2) (cv x3) (cfv (cv x1) cmee)) (co (cv x2) (cfv (cv x3) (cfv (cv x1) coc)) (cfv (cv x1) cmee)) (cfv (cv x1) cjn)))))) ⟶ wceq col (cin clat cops) ⟶ wceq coml (crab (λ x1 . wral (λ x2 . wral (λ x3 . wbr (cv x2) (cv x3) (cfv (cv x1) cple) ⟶ wceq (cv x3) (co (cv x2) (co (cv x3) (cfv (cv x2) (cfv (cv x1) coc)) (cfv (cv x1) cmee)) (cfv (cv x1) cjn))) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs)) (λ x1 . col)) ⟶ wceq ccvr (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . w3a (wa (wcel (cv x2) (cfv (cv x1) cbs)) (wcel (cv x3) (cfv (cv x1) cbs))) (wbr (cv x2) (cv x3) (cfv (cv x1) cplt)) (wn (wrex (λ x4 . wa (wbr (cv x2) (cv x4) (cfv (cv x1) cplt)) (wbr (cv x4) (cv x3) (cfv (cv x1) cplt))) (λ x4 . cfv (cv x1) cbs)))))) ⟶ wceq catm (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cfv (cv x1) cp0) (cv x2) (cfv (cv x1) ccvr)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq cal (crab (λ x1 . wa (wcel (cfv (cv x1) cbs) (cdm (cfv (cv x1) cglb))) (wral (λ x2 . wne (cv x2) (cfv (cv x1) cp0) ⟶ wrex (λ x3 . wbr (cv x3) (cv x2) (cfv (cv x1) cple)) (λ x3 . cfv (cv x1) catm)) (λ x2 . cfv (cv x1) cbs))) (λ x1 . clat)) ⟶ wceq clc (crab (λ x1 . wral (λ x2 . wral (λ x3 . wral (λ x4 . wa (wn (wbr (cv x2) (cv x4) (cfv (cv x1) cple))) (wbr (cv x2) (co (cv x4) (cv x3) (cfv (cv x1) cjn)) (cfv (cv x1) cple)) ⟶ wbr (cv x3) (co (cv x4) (cv x2) (cfv (cv x1) cjn)) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) catm)) (λ x2 . cfv (cv x1) catm)) (λ x1 . cal)) ⟶ wceq chlt (crab (λ x1 . wa (wral (λ x2 . wral (λ x3 . wne (cv x2) (cv x3) ⟶ wrex (λ x4 . w3a (wne (cv x4) (cv x2)) (wne (cv x4) (cv x3)) (wbr (cv x4) (co (cv x2) (cv x3) (cfv (cv x1) cjn)) (cfv (cv x1) cple))) (λ x4 . cfv (cv x1) catm)) (λ x3 . cfv (cv x1) catm)) (λ x2 . cfv (cv x1) catm)) (wrex (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (wa (wbr (cfv (cv x1) cp0) (cv x2) (cfv (cv x1) cplt)) (wbr (cv x2) (cv x3) (cfv (cv x1) cplt))) (wa (wbr (cv x3) (cv x4) (cfv (cv x1) cplt)) (wbr (cv x4) (cfv (cv x1) cp1) (cfv (cv x1) cplt)))) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) cbs)) (λ x2 . cfv (cv x1) cbs))) (λ x1 . cin (cin coml ccla) clc)) ⟶ wceq clln (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wrex (λ x3 . wbr (cv x3) (cv x2) (cfv (cv x1) ccvr)) (λ x3 . cfv (cv x1) catm)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq clpl (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wrex (λ x3 . wbr (cv x3) (cv x2) (cfv (cv x1) ccvr)) (λ x3 . cfv (cv x1) clln)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq clvol (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wrex (λ x3 . wbr (cv x3) (cv x2) (cfv (cv x1) ccvr)) (λ x3 . cfv (cv x1) clpl)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq clines (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (wne (cv x3) (cv x4)) (wceq (cv x2) (crab (λ x5 . wbr (cv x5) (co (cv x3) (cv x4) (cfv (cv x1) cjn)) (cfv (cv x1) cple)) (λ x5 . cfv (cv x1) catm)))) (λ x4 . cfv (cv x1) catm)) (λ x3 . cfv (cv x1) catm)))) ⟶ wceq cpointsN (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wrex (λ x3 . wceq (cv x2) (csn (cv x3))) (λ x3 . cfv (cv x1) catm)))) ⟶ wceq cpsubsp (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wa (wss (cv x2) (cfv (cv x1) catm)) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wbr (cv x5) (co (cv x3) (cv x4) (cfv (cv x1) cjn)) (cfv (cv x1) cple) ⟶ wcel (cv x5) (cv x2)) (λ x5 . cfv (cv x1) catm)) (λ x4 . cv x2)) (λ x3 . cv x2))))) ⟶ wceq cpmap (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) cbs) (λ x2 . crab (λ x3 . wbr (cv x3) (cv x2) (cfv (cv x1) cple)) (λ x3 . cfv (cv x1) catm)))) ⟶ wceq cpadd (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . cpw (cfv (cv x1) catm)) (λ x2 x3 . cpw (cfv (cv x1) catm)) (λ x2 x3 . cun (cun (cv x2) (cv x3)) (crab (λ x4 . wrex (λ x5 . wrex (λ x6 . wbr (cv x4) (co (cv x5) (cv x6) (cfv (cv x1) cjn)) (cfv (cv x1) cple)) (λ x6 . cv x3)) (λ x5 . cv x2)) (λ x4 . cfv (cv x1) catm))))) ⟶ wceq cpclN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) catm)) (λ x2 . cint (crab (λ x3 . wss (cv x2) (cv x3)) (λ x3 . cfv (cv x1) cpsubsp))))) ⟶ x0) ⟶ x0
Axiom df_polarityN__df_psubclN__df_lhyp__df_laut__df_watsN__df_pautN__df_ldil__df_ltrn__df_dilN__df_trnN__df_trl__df_tgrp__df_tendo__df_edring_rN__df_edring__df_dveca__df_disoa__df_dvech : ∀ x0 : ο . (wceq cpolN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cpw (cfv (cv x1) catm)) (λ x2 . cin (cfv (cv x1) catm) (ciin (λ x3 . cv x2) (λ x3 . cfv (cfv (cv x3) (cfv (cv x1) coc)) (cfv (cv x1) cpmap)))))) ⟶ wceq cpscN (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wa (wss (cv x2) (cfv (cv x1) catm)) (wceq (cfv (cfv (cv x2) (cfv (cv x1) cpolN)) (cfv (cv x1) cpolN)) (cv x2))))) ⟶ wceq clh (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cv x2) (cfv (cv x1) cp1) (cfv (cv x1) ccvr)) (λ x2 . cfv (cv x1) cbs))) ⟶ wceq claut (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wa (wf1o (cfv (cv x1) cbs) (cfv (cv x1) cbs) (cv x2)) (wral (λ x3 . wral (λ x4 . wb (wbr (cv x3) (cv x4) (cfv (cv x1) cple)) (wbr (cfv (cv x3) (cv x2)) (cfv (cv x4) (cv x2)) (cfv (cv x1) cple))) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) cbs))))) ⟶ wceq cwpointsN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) catm) (λ x2 . cdif (cfv (cv x1) catm) (cfv (csn (cv x2)) (cfv (cv x1) cpolN))))) ⟶ wceq cpautN (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wa (wf1o (cfv (cv x1) cpsubsp) (cfv (cv x1) cpsubsp) (cv x2)) (wral (λ x3 . wral (λ x4 . wb (wss (cv x3) (cv x4)) (wss (cfv (cv x3) (cv x2)) (cfv (cv x4) (cv x2)))) (λ x4 . cfv (cv x1) cpsubsp)) (λ x3 . cfv (cv x1) cpsubsp))))) ⟶ wceq cldil (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . crab (λ x3 . wral (λ x4 . wbr (cv x4) (cv x2) (cfv (cv x1) cple) ⟶ wceq (cfv (cv x4) (cv x3)) (cv x4)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . cfv (cv x1) claut)))) ⟶ wceq cltrn (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wa (wn (wbr (cv x4) (cv x2) (cfv (cv x1) cple))) (wn (wbr (cv x5) (cv x2) (cfv (cv x1) cple))) ⟶ wceq (co (co (cv x4) (cfv (cv x4) (cv x3)) (cfv (cv x1) cjn)) (cv x2) (cfv (cv x1) cmee)) (co (co (cv x5) (cfv (cv x5) (cv x3)) (cfv (cv x1) cjn)) (cv x2) (cfv (cv x1) cmee))) (λ x5 . cfv (cv x1) catm)) (λ x4 . cfv (cv x1) catm)) (λ x3 . cfv (cv x2) (cfv (cv x1) cldil))))) ⟶ wceq cdilN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) catm) (λ x2 . crab (λ x3 . wral (λ x4 . wss (cv x4) (cfv (cv x2) (cfv (cv x1) cwpointsN)) ⟶ wceq (cfv (cv x4) (cv x3)) (cv x4)) (λ x4 . cfv (cv x1) cpsubsp)) (λ x3 . cfv (cv x1) cpautN)))) ⟶ wceq ctrnN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) catm) (λ x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wceq (cin (co (cv x4) (cfv (cv x4) (cv x3)) (cfv (cv x1) cpadd)) (cfv (csn (cv x2)) (cfv (cv x1) cpolN))) (cin (co (cv x5) (cfv (cv x5) (cv x3)) (cfv (cv x1) cpadd)) (cfv (csn (cv x2)) (cfv (cv x1) cpolN)))) (λ x5 . cfv (cv x2) (cfv (cv x1) cwpointsN))) (λ x4 . cfv (cv x2) (cfv (cv x1) cwpointsN))) (λ x3 . cfv (cv x2) (cfv (cv x1) cdilN))))) ⟶ wceq ctrl (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 . crio (λ x4 . wral (λ x5 . wn (wbr (cv x5) (cv x2) (cfv (cv x1) cple)) ⟶ wceq (cv x4) (co (co (cv x5) (cfv (cv x5) (cv x3)) (cfv (cv x1) cjn)) (cv x2) (cfv (cv x1) cmee))) (λ x5 . cfv (cv x1) catm)) (λ x4 . cfv (cv x1) cbs))))) ⟶ wceq ctgrp (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cpr (cop (cfv cnx cbs) (cfv (cv x2) (cfv (cv x1) cltrn))) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 x4 . ccom (cv x3) (cv x4))))))) ⟶ wceq ctendo (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cab (λ x3 . w3a (wf (cfv (cv x2) (cfv (cv x1) cltrn)) (cfv (cv x2) (cfv (cv x1) cltrn)) (cv x3)) (wral (λ x4 . wral (λ x5 . wceq (cfv (ccom (cv x4) (cv x5)) (cv x3)) (ccom (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)))) (λ x5 . cfv (cv x2) (cfv (cv x1) cltrn))) (λ x4 . cfv (cv x2) (cfv (cv x1) cltrn))) (wral (λ x4 . wbr (cfv (cfv (cv x4) (cv x3)) (cfv (cv x2) (cfv (cv x1) ctrl))) (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) ctrl))) (cfv (cv x1) cple)) (λ x4 . cfv (cv x2) (cfv (cv x1) cltrn))))))) ⟶ wceq cedring_rN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . ctp (cop (cfv cnx cbs) (cfv (cv x2) (cfv (cv x1) ctendo))) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cmpt (λ x5 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x5 . ccom (cfv (cv x5) (cv x3)) (cfv (cv x5) (cv x4)))))) (cop (cfv cnx cmulr) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . ccom (cv x4) (cv x3))))))) ⟶ wceq cedring (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . ctp (cop (cfv cnx cbs) (cfv (cv x2) (cfv (cv x1) ctendo))) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cmpt (λ x5 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x5 . ccom (cfv (cv x5) (cv x3)) (cfv (cv x5) (cv x4)))))) (cop (cfv cnx cmulr) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . ccom (cv x3) (cv x4))))))) ⟶ wceq cdveca (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cun (ctp (cop (cfv cnx cbs) (cfv (cv x2) (cfv (cv x1) cltrn))) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 x4 . ccom (cv x3) (cv x4)))) (cop (cfv cnx csca) (cfv (cv x2) (cfv (cv x1) cedring)))) (csn (cop (cfv cnx cvsca) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x3 x4 . cfv (cv x4) (cv x3)))))))) ⟶ wceq cdia (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . crab (λ x4 . wbr (cv x4) (cv x2) (cfv (cv x1) cple)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . crab (λ x4 . wbr (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) ctrl))) (cv x3) (cfv (cv x1) cple)) (λ x4 . cfv (cv x2) (cfv (cv x1) cltrn)))))) ⟶ wceq cdvh (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cun (ctp (cop (cfv cnx cbs) (cxp (cfv (cv x2) (cfv (cv x1) cltrn)) (cfv (cv x2) (cfv (cv x1) ctendo)))) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cxp (cfv (cv x2) (cfv (cv x1) cltrn)) (cfv (cv x2) (cfv (cv x1) ctendo))) (λ x3 x4 . cxp (cfv (cv x2) (cfv (cv x1) cltrn)) (cfv (cv x2) (cfv (cv x1) ctendo))) (λ x3 x4 . cop (ccom (cfv (cv x3) c1st) (cfv (cv x4) c1st)) (cmpt (λ x5 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x5 . ccom (cfv (cv x5) (cfv (cv x3) c2nd)) (cfv (cv x5) (cfv (cv x4) c2nd))))))) (cop (cfv cnx csca) (cfv (cv x2) (cfv (cv x1) cedring)))) (csn (cop (cfv cnx cvsca) (cmpt2 (λ x3 x4 . cfv (cv x2) (cfv (cv x1) ctendo)) (λ x3 x4 . cxp (cfv (cv x2) (cfv (cv x1) cltrn)) (cfv (cv x2) (cfv (cv x1) ctendo))) (λ x3 x4 . cop (cfv (cfv (cv x4) c1st) (cv x3)) (ccom (cv x3) (cfv (cv x4) c2nd))))))))) ⟶ x0) ⟶ x0
Axiom df_docaN__df_djaN__df_dib__df_dic__df_dih__df_doch__df_djh__df_lpolN__df_lcdual__df_mapd__df_hvmap__df_hdmap1__df_hdmap__df_hgmap__df_hlhil__df_nacs__df_mzpcl__df_mzp : ∀ x0 : ο . (wceq cocaN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cpw (cfv (cv x2) (cfv (cv x1) cltrn))) (λ x3 . cfv (co (co (cfv (cfv (cint (crab (λ x4 . wss (cv x3) (cv x4)) (λ x4 . crn (cfv (cv x2) (cfv (cv x1) cdia))))) (ccnv (cfv (cv x2) (cfv (cv x1) cdia)))) (cfv (cv x1) coc)) (cfv (cv x2) (cfv (cv x1) coc)) (cfv (cv x1) cjn)) (cv x2) (cfv (cv x1) cmee)) (cfv (cv x2) (cfv (cv x1) cdia)))))) ⟶ wceq cdjaN (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt2 (λ x3 x4 . cpw (cfv (cv x2) (cfv (cv x1) cltrn))) (λ x3 x4 . cpw (cfv (cv x2) (cfv (cv x1) cltrn))) (λ x3 x4 . cfv (cin (cfv (cv x3) (cfv (cv x2) (cfv (cv x1) cocaN))) (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) cocaN)))) (cfv (cv x2) (cfv (cv x1) cocaN)))))) ⟶ wceq cdib (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cdm (cfv (cv x2) (cfv (cv x1) cdia))) (λ x3 . cxp (cfv (cv x3) (cfv (cv x2) (cfv (cv x1) cdia))) (csn (cmpt (λ x4 . cfv (cv x2) (cfv (cv x1) cltrn)) (λ x4 . cres cid (cfv (cv x1) cbs)))))))) ⟶ wceq cdic (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . crab (λ x4 . wn (wbr (cv x4) (cv x2) (cfv (cv x1) cple))) (λ x4 . cfv (cv x1) catm)) (λ x3 . copab (λ x4 x5 . wa (wceq (cv x4) (cfv (crio (λ x6 . wceq (cfv (cfv (cv x2) (cfv (cv x1) coc)) (cv x6)) (cv x3)) (λ x6 . cfv (cv x2) (cfv (cv x1) cltrn))) (cv x5))) (wcel (cv x5) (cfv (cv x2) (cfv (cv x1) ctendo)))))))) ⟶ wceq cdih (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cfv (cv x1) cbs) (λ x3 . cif (wbr (cv x3) (cv x2) (cfv (cv x1) cple)) (cfv (cv x3) (cfv (cv x2) (cfv (cv x1) cdib))) (crio (λ x4 . wral (λ x5 . wa (wn (wbr (cv x5) (cv x2) (cfv (cv x1) cple))) (wceq (co (cv x5) (co (cv x3) (cv x2) (cfv (cv x1) cmee)) (cfv (cv x1) cjn)) (cv x3)) ⟶ wceq (cv x4) (co (cfv (cv x5) (cfv (cv x2) (cfv (cv x1) cdic))) (cfv (co (cv x3) (cv x2) (cfv (cv x1) cmee)) (cfv (cv x2) (cfv (cv x1) cdib))) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clsm))) (λ x5 . cfv (cv x1) catm)) (λ x4 . cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clss)))))) ⟶ wceq coch (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cpw (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cbs)) (λ x3 . cfv (cfv (cfv (crab (λ x4 . wss (cv x3) (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) cdih)))) (λ x4 . cfv (cv x1) cbs)) (cfv (cv x1) cglb)) (cfv (cv x1) coc)) (cfv (cv x2) (cfv (cv x1) cdih)))))) ⟶ wceq cdjh (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt2 (λ x3 x4 . cpw (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cbs)) (λ x3 x4 . cpw (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cbs)) (λ x3 x4 . cfv (cin (cfv (cv x3) (cfv (cv x2) (cfv (cv x1) coch))) (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) coch)))) (cfv (cv x2) (cfv (cv x1) coch)))))) ⟶ wceq clpoN (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . w3a (wceq (cfv (cfv (cv x1) cbs) (cv x2)) (csn (cfv (cv x1) c0g))) (∀ x3 x4 . w3a (wss (cv x3) (cfv (cv x1) cbs)) (wss (cv x4) (cfv (cv x1) cbs)) (wss (cv x3) (cv x4)) ⟶ wss (cfv (cv x4) (cv x2)) (cfv (cv x3) (cv x2))) (wral (λ x3 . wa (wcel (cfv (cv x3) (cv x2)) (cfv (cv x1) clsh)) (wceq (cfv (cfv (cv x3) (cv x2)) (cv x2)) (cv x3))) (λ x3 . cfv (cv x1) clsa))) (λ x2 . co (cfv (cv x1) clss) (cpw (cfv (cv x1) cbs)) cmap))) ⟶ wceq clcd (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . co (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cld) (crab (λ x3 . wceq (cfv (cfv (cfv (cv x3) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clk)) (cfv (cv x2) (cfv (cv x1) coch))) (cfv (cv x2) (cfv (cv x1) coch))) (cfv (cv x3) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clk))) (λ x3 . cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clfn)) cress))) ⟶ wceq cmpd (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clss) (λ x3 . crab (λ x4 . wa (wceq (cfv (cfv (cfv (cv x4) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clk)) (cfv (cv x2) (cfv (cv x1) coch))) (cfv (cv x2) (cfv (cv x1) coch))) (cfv (cv x4) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clk))) (wss (cfv (cfv (cv x4) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clk)) (cfv (cv x2) (cfv (cv x1) coch))) (cv x3))) (λ x4 . cfv (cfv (cv x2) (cfv (cv x1) cdvh)) clfn))))) ⟶ wceq chvm (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cmpt (λ x3 . cdif (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cbs) (csn (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) c0g))) (λ x3 . cmpt (λ x4 . cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cbs) (λ x4 . crio (λ x5 . wrex (λ x6 . wceq (cv x4) (co (cv x6) (co (cv x5) (cv x3) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cvsca)) (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) cplusg))) (λ x6 . cfv (csn (cv x3)) (cfv (cv x2) (cfv (cv x1) coch)))) (λ x5 . cfv (cfv (cfv (cv x2) (cfv (cv x1) cdvh)) csca) cbs)))))) ⟶ wceq chdma1 (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cab (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wsbc (λ x7 . wsbc (λ x8 . wsbc (λ x9 . wsbc (λ x10 . wcel (cv x3) (cmpt (λ x11 . cxp (cxp (cv x5) (cv x8)) (cv x5)) (λ x11 . cif (wceq (cfv (cv x11) c2nd) (cfv (cv x4) c0g)) (cfv (cv x7) c0g) (crio (λ x12 . wa (wceq (cfv (cfv (csn (cfv (cv x11) c2nd)) (cv x6)) (cv x10)) (cfv (csn (cv x12)) (cv x9))) (wceq (cfv (cfv (csn (co (cfv (cfv (cv x11) c1st) c1st) (cfv (cv x11) c2nd) (cfv (cv x4) csg))) (cv x6)) (cv x10)) (cfv (csn (co (cfv (cfv (cv x11) c1st) c2nd) (cv x12) (cfv (cv x7) csg))) (cv x9)))) (λ x12 . cv x8))))) (cfv (cv x2) (cfv (cv x1) cmpd))) (cfv (cv x7) clspn)) (cfv (cv x7) cbs)) (cfv (cv x2) (cfv (cv x1) clcd))) (cfv (cv x4) clspn)) (cfv (cv x4) cbs)) (cfv (cv x2) (cfv (cv x1) cdvh)))))) ⟶ wceq chdma (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cab (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wsbc (λ x7 . wcel (cv x3) (cmpt (λ x8 . cv x6) (λ x8 . crio (λ x9 . wral (λ x10 . wn (wcel (cv x10) (cun (cfv (csn (cv x4)) (cfv (cv x5) clspn)) (cfv (csn (cv x8)) (cfv (cv x5) clspn)))) ⟶ wceq (cv x9) (cfv (cotp (cv x10) (cfv (cotp (cv x4) (cfv (cv x4) (cfv (cv x2) (cfv (cv x1) chvm))) (cv x10)) (cv x7)) (cv x8)) (cv x7))) (λ x10 . cv x6)) (λ x9 . cfv (cfv (cv x2) (cfv (cv x1) clcd)) cbs)))) (cfv (cv x2) (cfv (cv x1) chdma1))) (cfv (cv x5) cbs)) (cfv (cv x2) (cfv (cv x1) cdvh))) (cop (cres cid (cfv (cv x1) cbs)) (cres cid (cfv (cv x2) (cfv (cv x1) cltrn)))))))) ⟶ wceq chg (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . cab (λ x3 . wsbc (λ x4 . wsbc (λ x5 . wsbc (λ x6 . wcel (cv x3) (cmpt (λ x7 . cv x5) (λ x7 . crio (λ x8 . wral (λ x9 . wceq (cfv (co (cv x7) (cv x9) (cfv (cv x4) cvsca)) (cv x6)) (co (cv x8) (cfv (cv x9) (cv x6)) (cfv (cfv (cv x2) (cfv (cv x1) clcd)) cvsca))) (λ x9 . cfv (cv x4) cbs)) (λ x8 . cv x5)))) (cfv (cv x2) (cfv (cv x1) chdma))) (cfv (cfv (cv x4) csca) cbs)) (cfv (cv x2) (cfv (cv x1) cdvh)))))) ⟶ wceq chlh (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cv x1) clh) (λ x2 . csb (cfv (cv x2) (cfv (cv x1) cdvh)) (λ x3 . csb (cfv (cv x3) cbs) (λ x4 . cun (ctp (cop (cfv cnx cbs) (cv x4)) (cop (cfv cnx cplusg) (cfv (cv x3) cplusg)) (cop (cfv cnx csca) (co (cfv (cv x2) (cfv (cv x1) cedring)) (cop (cfv cnx cstv) (cfv (cv x2) (cfv (cv x1) chg))) csts))) (cpr (cop (cfv cnx cvsca) (cfv (cv x3) cvsca)) (cop (cfv cnx cip) (cmpt2 (λ x5 x6 . cv x4) (λ x5 x6 . cv x4) (λ x5 x6 . cfv (cv x5) (cfv (cv x6) (cfv (cv x2) (cfv (cv x1) chdma)))))))))))) ⟶ wceq cnacs (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wral (λ x3 . wrex (λ x4 . wceq (cv x3) (cfv (cv x4) (cfv (cv x2) cmrc))) (λ x4 . cin (cpw (cv x1)) cfn)) (λ x3 . cv x2)) (λ x2 . cfv (cv x1) cacs))) ⟶ wceq cmzpcl (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wa (wa (wral (λ x3 . wcel (cxp (co cz (cv x1) cmap) (csn (cv x3))) (cv x2)) (λ x3 . cz)) (wral (λ x3 . wcel (cmpt (λ x4 . co cz (cv x1) cmap) (λ x4 . cfv (cv x3) (cv x4))) (cv x2)) (λ x3 . cv x1))) (wral (λ x3 . wral (λ x4 . wa (wcel (co (cv x3) (cv x4) (cof caddc)) (cv x2)) (wcel (co (cv x3) (cv x4) (cof cmul)) (cv x2))) (λ x4 . cv x2)) (λ x3 . cv x2))) (λ x2 . cpw (co cz (co cz (cv x1) cmap) cmap)))) ⟶ wceq cmzp (cmpt (λ x1 . cvv) (λ x1 . cint (cfv (cv x1) cmzpcl))) ⟶ x0) ⟶ x0
Axiom df_dioph__df_squarenn__df_pell1qr__df_pell14qr__df_pell1234qr__df_pellfund__df_rmx__df_rmy__df_lfig__df_lnm__df_lnr__df_ldgis__df_mnc__df_plylt__df_dgraa__df_mpaa__df_itgo__df_za : ∀ x0 : ο . (wceq cdioph (cmpt (λ x1 . cn0) (λ x1 . crn (cmpt2 (λ x2 x3 . cfv (cv x1) cuz) (λ x2 x3 . cfv (co c1 (cv x2) cfz) cmzp) (λ x2 x3 . cab (λ x4 . wrex (λ x5 . wa (wceq (cv x4) (cres (cv x5) (co c1 (cv x1) cfz))) (wceq (cfv (cv x5) (cv x3)) cc0)) (λ x5 . co cn0 (co c1 (cv x2) cfz) cmap)))))) ⟶ wceq csquarenn (crab (λ x1 . wcel (cfv (cv x1) csqrt) cq) (λ x1 . cn)) ⟶ wceq cpell1qr (cmpt (λ x1 . cdif cn csquarenn) (λ x1 . crab (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (wceq (cv x2) (co (cv x3) (co (cfv (cv x1) csqrt) (cv x4) cmul) caddc)) (wceq (co (co (cv x3) c2 cexp) (co (cv x1) (co (cv x4) c2 cexp) cmul) cmin) c1)) (λ x4 . cn0)) (λ x3 . cn0)) (λ x2 . cr))) ⟶ wceq cpell14qr (cmpt (λ x1 . cdif cn csquarenn) (λ x1 . crab (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (wceq (cv x2) (co (cv x3) (co (cfv (cv x1) csqrt) (cv x4) cmul) caddc)) (wceq (co (co (cv x3) c2 cexp) (co (cv x1) (co (cv x4) c2 cexp) cmul) cmin) c1)) (λ x4 . cz)) (λ x3 . cn0)) (λ x2 . cr))) ⟶ wceq cpell1234qr (cmpt (λ x1 . cdif cn csquarenn) (λ x1 . crab (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (wceq (cv x2) (co (cv x3) (co (cfv (cv x1) csqrt) (cv x4) cmul) caddc)) (wceq (co (co (cv x3) c2 cexp) (co (cv x1) (co (cv x4) c2 cexp) cmul) cmin) c1)) (λ x4 . cz)) (λ x3 . cz)) (λ x2 . cr))) ⟶ wceq cpellfund (cmpt (λ x1 . cdif cn csquarenn) (λ x1 . cinf (crab (λ x2 . wbr c1 (cv x2) clt) (λ x2 . cfv (cv x1) cpell14qr)) cr clt)) ⟶ wceq crmx (cmpt2 (λ x1 x2 . cfv c2 cuz) (λ x1 x2 . cz) (λ x1 x2 . cfv (cfv (co (co (cv x1) (cfv (co (co (cv x1) c2 cexp) c1 cmin) csqrt) caddc) (cv x2) cexp) (ccnv (cmpt (λ x3 . cxp cn0 cz) (λ x3 . co (cfv (cv x3) c1st) (co (cfv (co (co (cv x1) c2 cexp) c1 cmin) csqrt) (cfv (cv x3) c2nd) cmul) caddc)))) c1st)) ⟶ wceq crmy (cmpt2 (λ x1 x2 . cfv c2 cuz) (λ x1 x2 . cz) (λ x1 x2 . cfv (cfv (co (co (cv x1) (cfv (co (co (cv x1) c2 cexp) c1 cmin) csqrt) caddc) (cv x2) cexp) (ccnv (cmpt (λ x3 . cxp cn0 cz) (λ x3 . co (cfv (cv x3) c1st) (co (cfv (co (co (cv x1) c2 cexp) c1 cmin) csqrt) (cfv (cv x3) c2nd) cmul) caddc)))) c2nd)) ⟶ wceq clfig (crab (λ x1 . wcel (cfv (cv x1) cbs) (cima (cfv (cv x1) clspn) (cin (cpw (cfv (cv x1) cbs)) cfn))) (λ x1 . clmod)) ⟶ wceq clnm (crab (λ x1 . wral (λ x2 . wcel (co (cv x1) (cv x2) cress) clfig) (λ x2 . cfv (cv x1) clss)) (λ x1 . clmod)) ⟶ wceq clnr (crab (λ x1 . wcel (cfv (cv x1) crglmod) clnm) (λ x1 . crg)) ⟶ wceq cldgis (cmpt (λ x1 . cvv) (λ x1 . cmpt (λ x2 . cfv (cfv (cv x1) cpl1) clidl) (λ x2 . cmpt (λ x3 . cn0) (λ x3 . cab (λ x4 . wrex (λ x5 . wa (wbr (cfv (cv x5) (cfv (cv x1) cdg1)) (cv x3) cle) (wceq (cv x4) (cfv (cv x3) (cfv (cv x5) cco1)))) (λ x5 . cv x2)))))) ⟶ wceq cmnc (cmpt (λ x1 . cpw cc) (λ x1 . crab (λ x2 . wceq (cfv (cfv (cv x2) cdgr) (cfv (cv x2) ccoe)) c1) (λ x2 . cfv (cv x1) cply))) ⟶ wceq cplylt (cmpt2 (λ x1 x2 . cpw cc) (λ x1 x2 . cn0) (λ x1 x2 . crab (λ x3 . wo (wceq (cv x3) c0p) (wbr (cfv (cv x3) cdgr) (cv x2) clt)) (λ x3 . cfv (cv x1) cply))) ⟶ wceq cdgraa (cmpt (λ x1 . caa) (λ x1 . cinf (crab (λ x2 . wrex (λ x3 . wa (wceq (cfv (cv x3) cdgr) (cv x2)) (wceq (cfv (cv x1) (cv x3)) cc0)) (λ x3 . cdif (cfv cq cply) (csn c0p))) (λ x2 . cn)) cr clt)) ⟶ wceq cmpaa (cmpt (λ x1 . caa) (λ x1 . crio (λ x2 . w3a (wceq (cfv (cv x2) cdgr) (cfv (cv x1) cdgraa)) (wceq (cfv (cv x1) (cv x2)) cc0) (wceq (cfv (cfv (cv x1) cdgraa) (cfv (cv x2) ccoe)) c1)) (λ x2 . cfv cq cply))) ⟶ wceq citgo (cmpt (λ x1 . cpw cc) (λ x1 . crab (λ x2 . wrex (λ x3 . wa (wceq (cfv (cv x2) (cv x3)) cc0) (wceq (cfv (cfv (cv x3) cdgr) (cfv (cv x3) ccoe)) c1)) (λ x3 . cfv (cv x1) cply)) (λ x2 . cc))) ⟶ wceq cza (cfv cz citgo) ⟶ x0) ⟶ x0
Axiom df_mend__df_sdrg__df_cytp__df_topsep__df_toplnd__df_rcl__df_he__ax_frege1__ax_frege2__ax_frege8__ax_frege28__ax_frege31__ax_frege41__ax_frege52a__ax_frege54a__ax_frege58a__ax_frege52c__ax_frege54c : ∀ x0 : ο . (wceq cmend (cmpt (λ x1 . cvv) (λ x1 . csb (co (cv x1) (cv x1) clmhm) (λ x2 . cun (ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx cplusg) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . co (cv x3) (cv x4) (cof (cfv (cv x1) cplusg))))) (cop (cfv cnx cmulr) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . ccom (cv x3) (cv x4))))) (cpr (cop (cfv cnx csca) (cfv (cv x1) csca)) (cop (cfv cnx cvsca) (cmpt2 (λ x3 x4 . cfv (cfv (cv x1) csca) cbs) (λ x3 x4 . cv x2) (λ x3 x4 . co (cxp (cfv (cv x1) cbs) (csn (cv x3))) (cv x4) (cof (cfv (cv x1) cvsca))))))))) ⟶ wceq csdrg (cmpt (λ x1 . cdr) (λ x1 . crab (λ x2 . wcel (co (cv x1) (cv x2) cress) cdr) (λ x2 . cfv (cv x1) csubrg))) ⟶ wceq ccytp (cmpt (λ x1 . cn) (λ x1 . co (cfv (cfv ccnfld cpl1) cmgp) (cmpt (λ x2 . cima (ccnv (cfv (co (cfv ccnfld cmgp) (cdif cc (csn cc0)) cress) cod)) (csn (cv x1))) (λ x2 . co (cfv ccnfld cv1) (cfv (cv x2) (cfv (cfv ccnfld cpl1) cascl)) (cfv (cfv ccnfld cpl1) csg))) cgsu)) ⟶ wceq ctopsep (crab (λ x1 . wrex (λ x2 . wa (wbr (cv x2) com cdom) (wceq (cfv (cv x2) (cfv (cv x1) ccl)) (cuni (cv x1)))) (λ x2 . cpw (cuni (cv x1)))) (λ x1 . ctop)) ⟶ wceq ctoplnd (crab (λ x1 . wral (λ x2 . wceq (cuni (cv x1)) (cuni (cv x2)) ⟶ wrex (λ x3 . wa (wbr (cv x3) com cdom) (wceq (cuni (cv x1)) (cuni (cv x3)))) (λ x3 . cpw (cv x1))) (λ x2 . cpw (cv x1))) (λ x1 . ctop)) ⟶ wceq crcl (cmpt (λ x1 . cvv) (λ x1 . cint (cab (λ x2 . wa (wss (cv x1) (cv x2)) (wss (cres cid (cun (cdm (cv x2)) (crn (cv x2)))) (cv x2)))))) ⟶ (∀ x1 x2 : ι → ο . wb (whe x1 x2) (wss (cima x2 x1) x1)) ⟶ (∀ x1 x2 : ο . x1 ⟶ x2 ⟶ x1) ⟶ (∀ x1 x2 x3 : ο . (x1 ⟶ x2 ⟶ x3) ⟶ (x1 ⟶ x2) ⟶ x1 ⟶ x3) ⟶ (∀ x1 x2 x3 : ο . (x1 ⟶ x2 ⟶ x3) ⟶ x2 ⟶ x1 ⟶ x3) ⟶ (∀ x1 x2 : ο . (x1 ⟶ x2) ⟶ wn x2 ⟶ wn x1) ⟶ (∀ x1 : ο . wn (wn x1) ⟶ x1) ⟶ (∀ x1 : ο . x1 ⟶ wn (wn x1)) ⟶ (∀ x1 x2 x3 x4 : ο . wb x1 x2 ⟶ wif x1 x4 x3 ⟶ wif x2 x4 x3) ⟶ (∀ x1 : ο . wb x1 x1) ⟶ (∀ x1 x2 x3 : ο . wa x2 x3 ⟶ wif x1 x2 x3) ⟶ (∀ x1 : ι → ο . ∀ x2 x3 : ι → ι → ο . ∀ x4 . wceq (x2 x4) (x3 x4) ⟶ wsbc x1 (x2 x4) ⟶ wsbc x1 (x3 x4)) ⟶ (∀ x1 : ι → ο . wceq x1 x1) ⟶ x0) ⟶ x0
Axiom ax_frege58b__ax_frege58b_b__df_bcc__df_addr__df_subr__df_mulv__df_ptdf__df_rr3__df_line3__df_vd1__df_vd2__df_vhc2__df_vhc3__df_vd3__df_liminf__df_xlim__df_salg__df_salon : ∀ x0 : ο . ((∀ x1 : ι → ο . ∀ x2 . (∀ x3 . x1 x3) ⟶ wsb x1 x2) ⟶ (∀ x1 : ι → ο . ∀ x2 . (∀ x3 . x1 x3) ⟶ wsb x1 x2) ⟶ wceq cbcc (cmpt2 (λ x1 x2 . cc) (λ x1 x2 . cn0) (λ x1 x2 . co (co (cv x1) (cv x2) cfallfac) (cfv (cv x2) cfa) cdiv)) ⟶ wceq cplusr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cr) (λ x3 . co (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) caddc))) ⟶ wceq cminusr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cr) (λ x3 . co (cfv (cv x3) (cv x1)) (cfv (cv x3) (cv x2)) cmin))) ⟶ wceq ctimesr (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt (λ x3 . cr) (λ x3 . co (cv x1) (cfv (cv x3) (cv x2)) cmul))) ⟶ (∀ x1 x2 : ι → ο . wceq (cptdfc x1 x2) (cmpt (λ x3 . cr) (λ x3 . cima (co (co (cv x3) (co x2 x1 cminusr) ctimesr) x1 cpv) (ctp c1 c2 c3)))) ⟶ wceq crr3c (co cr (ctp c1 c2 c3) cmap) ⟶ wceq cline3 (crab (λ x1 . wa (wbr c2o (cv x1) cdom) (wral (λ x2 . wral (λ x3 . wne (cv x3) (cv x2) ⟶ wceq (crn (cptdfc (cv x2) (cv x3))) (cv x1)) (λ x3 . cv x1)) (λ x2 . cv x1))) (λ x1 . cpw crr3c)) ⟶ (∀ x1 x2 : ο . wb (wvd1 x1 x2) (x1 ⟶ x2)) ⟶ (∀ x1 x2 x3 : ο . wb (wvd2 x1 x2 x3) (wa x1 x2 ⟶ x3)) ⟶ (∀ x1 x2 : ο . wb (wvhc2 x1 x2) (wa x1 x2)) ⟶ (∀ x1 x2 x3 : ο . wb (wvhc3 x1 x2 x3) (w3a x1 x2 x3)) ⟶ (∀ x1 x2 x3 x4 : ο . wb (wvd3 x1 x2 x3 x4) (w3a x1 x2 x3 ⟶ x4)) ⟶ wceq clsi (cmpt (λ x1 . cvv) (λ x1 . csup (crn (cmpt (λ x2 . cr) (λ x2 . cinf (cin (cima (cv x1) (co (cv x2) cpnf cico)) cxr) cxr clt))) cxr clt)) ⟶ wceq clsxlim (cfv (cfv cle cordt) clm) ⟶ wceq csalg (cab (λ x1 . w3a (wcel c0 (cv x1)) (wral (λ x2 . wcel (cdif (cuni (cv x1)) (cv x2)) (cv x1)) (λ x2 . cv x1)) (wral (λ x2 . wbr (cv x2) com cdom ⟶ wcel (cuni (cv x2)) (cv x1)) (λ x2 . cpw (cv x1))))) ⟶ wceq csalon (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wceq (cuni (cv x2)) (cv x1)) (λ x2 . csalg))) ⟶ x0) ⟶ x0
Axiom df_salgen__df_sumge0__df_mea__df_ome__df_caragen__df_ovoln__df_voln__df_smblfn__df_dfat__df_afv__df_aov__df_nelbr__df_iccp__df_pfx__df_fmtno__df_even__df_odd__df_gbe : ∀ x0 : ο . (wceq csalgen (cmpt (λ x1 . cvv) (λ x1 . cint (crab (λ x2 . wa (wceq (cuni (cv x2)) (cuni (cv x1))) (wss (cv x1) (cv x2))) (λ x2 . csalg)))) ⟶ wceq csumge0 (cmpt (λ x1 . cvv) (λ x1 . cif (wcel cpnf (crn (cv x1))) cpnf (csup (crn (cmpt (λ x2 . cin (cpw (cdm (cv x1))) cfn) (λ x2 . csu (cv x2) (λ x3 . cfv (cv x3) (cv x1))))) cxr clt))) ⟶ wceq cmea (cab (λ x1 . wa (wa (wa (wf (cdm (cv x1)) (co cc0 cpnf cicc) (cv x1)) (wcel (cdm (cv x1)) csalg)) (wceq (cfv c0 (cv x1)) cc0)) (wral (λ x2 . wa (wbr (cv x2) com cdom) (wdisj (λ x3 . cv x2) cv) ⟶ wceq (cfv (cuni (cv x2)) (cv x1)) (cfv (cres (cv x1) (cv x2)) csumge0)) (λ x2 . cpw (cdm (cv x1)))))) ⟶ wceq come (cab (λ x1 . wa (wa (wa (wa (wf (cdm (cv x1)) (co cc0 cpnf cicc) (cv x1)) (wceq (cdm (cv x1)) (cpw (cuni (cdm (cv x1)))))) (wceq (cfv c0 (cv x1)) cc0)) (wral (λ x2 . wral (λ x3 . wbr (cfv (cv x3) (cv x1)) (cfv (cv x2) (cv x1)) cle) (λ x3 . cpw (cv x2))) (λ x2 . cpw (cuni (cdm (cv x1)))))) (wral (λ x2 . wbr (cv x2) com cdom ⟶ wbr (cfv (cuni (cv x2)) (cv x1)) (cfv (cres (cv x1) (cv x2)) csumge0) cle) (λ x2 . cpw (cdm (cv x1)))))) ⟶ wceq ccaragen (cmpt (λ x1 . come) (λ x1 . crab (λ x2 . wral (λ x3 . wceq (co (cfv (cin (cv x3) (cv x2)) (cv x1)) (cfv (cdif (cv x3) (cv x2)) (cv x1)) cxad) (cfv (cv x3) (cv x1))) (λ x3 . cpw (cuni (cdm (cv x1))))) (λ x2 . cpw (cuni (cdm (cv x1)))))) ⟶ wceq covoln (cmpt (λ x1 . cfn) (λ x1 . cmpt (λ x2 . cpw (co cr (cv x1) cmap)) (λ x2 . cif (wceq (cv x1) c0) cc0 (cinf (crab (λ x3 . wrex (λ x4 . wa (wss (cv x2) (ciun (λ x5 . cn) (λ x5 . cixp (λ x6 . cv x1) (λ x6 . cfv (cv x6) (ccom cico (cfv (cv x5) (cv x4))))))) (wceq (cv x3) (cfv (cmpt (λ x5 . cn) (λ x5 . cprod (λ x6 . cv x1) (λ x6 . cfv (cfv (cv x6) (ccom cico (cfv (cv x5) (cv x4)))) cvol))) csumge0))) (λ x4 . co (co (cxp cr cr) (cv x1) cmap) cn cmap)) (λ x3 . cxr)) cxr clt)))) ⟶ wceq cvoln (cmpt (λ x1 . cfn) (λ x1 . cres (cfv (cv x1) covoln) (cfv (cfv (cv x1) covoln) ccaragen))) ⟶ wceq csmblfn (cmpt (λ x1 . csalg) (λ x1 . crab (λ x2 . wral (λ x3 . wcel (cima (ccnv (cv x2)) (co cmnf (cv x3) cioo)) (co (cv x1) (cdm (cv x2)) crest)) (λ x3 . cr)) (λ x2 . co cr (cuni (cv x1)) cpm))) ⟶ (∀ x1 x2 : ι → ο . wb (wdfat x1 x2) (wa (wcel x1 (cdm x2)) (wfun (cres x2 (csn x1))))) ⟶ (∀ x1 x2 : ι → ο . wceq (cafv x1 x2) (cif (wdfat x1 x2) (cio (λ x3 . wbr x1 (cv x3) x2)) cvv)) ⟶ (∀ x1 x2 x3 : ι → ο . wceq (caov x1 x2 x3) (cafv (cop x1 x2) x3)) ⟶ wceq cnelbr (copab (λ x1 x2 . wn (wcel (cv x1) (cv x2)))) ⟶ wceq ciccp (cmpt (λ x1 . cn) (λ x1 . crab (λ x2 . wral (λ x3 . wbr (cfv (cv x3) (cv x2)) (cfv (co (cv x3) c1 caddc) (cv x2)) clt) (λ x3 . co cc0 (cv x1) cfzo)) (λ x2 . co cxr (co cc0 (cv x1) cfz) cmap))) ⟶ wceq cpfx (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cn0) (λ x1 x2 . co (cv x1) (cop cc0 (cv x2)) csubstr)) ⟶ wceq cfmtno (cmpt (λ x1 . cn0) (λ x1 . co (co c2 (co c2 (cv x1) cexp) cexp) c1 caddc)) ⟶ wceq ceven (crab (λ x1 . wcel (co (cv x1) c2 cdiv) cz) (λ x1 . cz)) ⟶ wceq codd (crab (λ x1 . wcel (co (co (cv x1) c1 caddc) c2 cdiv) cz) (λ x1 . cz)) ⟶ wceq cgbe (crab (λ x1 . wrex (λ x2 . wrex (λ x3 . w3a (wcel (cv x2) codd) (wcel (cv x3) codd) (wceq (cv x1) (co (cv x2) (cv x3) caddc))) (λ x3 . cprime)) (λ x2 . cprime)) (λ x1 . ceven)) ⟶ x0) ⟶ x0
Axiom df_gbow__df_gbo__ax_bgbltosilva__ax_tgoldbachgt__ax_hgprmladder__ax_bgbltosilvaOLD__ax_hgprmladderOLD__ax_tgoldbachgtOLD__df_upwlks__df_spr__df_mgmhm__df_submgm__df_cllaw__df_comlaw__df_asslaw__df_intop__df_clintop__df_assintop : ∀ x0 : ο . (wceq cgbow (crab (λ x1 . wrex (λ x2 . wrex (λ x3 . wrex (λ x4 . wceq (cv x1) (co (co (cv x2) (cv x3) caddc) (cv x4) caddc)) (λ x4 . cprime)) (λ x3 . cprime)) (λ x2 . cprime)) (λ x1 . codd)) ⟶ wceq cgbo (crab (λ x1 . wrex (λ x2 . wrex (λ x3 . wrex (λ x4 . wa (w3a (wcel (cv x2) codd) (wcel (cv x3) codd) (wcel (cv x4) codd)) (wceq (cv x1) (co (co (cv x2) (cv x3) caddc) (cv x4) caddc))) (λ x4 . cprime)) (λ x3 . cprime)) (λ x2 . cprime)) (λ x1 . codd)) ⟶ (∀ x1 : ι → ο . w3a (wcel x1 ceven) (wbr c4 x1 clt) (wbr x1 (co c4 (co (cdc c1 cc0) (cdc c1 c8) cexp) cmul) cle) ⟶ wcel x1 cgbe) ⟶ (∀ x1 : ι → ι → ι → ι → ι → ι → ο . ∀ x2 : ι → ι → ο . (∀ x3 . wceq (x2 x3) (crab (λ x4 . wn (wbr c2 (cv x4) cdvds)) (λ x4 . cz))) ⟶ (∀ x3 x4 x5 x6 x7 . wceq (x1 x3 x4 x5 x6 x7) (crab (λ x8 . wrex (λ x9 . wrex (λ x10 . wrex (λ x11 . wa (w3a (wcel (cv x9) (x2 x4)) (wcel (cv x10) (x2 x4)) (wcel (cv x11) (x2 x4))) (wceq (cv x8) (co (co (cv x9) (cv x10) caddc) (cv x11) caddc))) (λ x11 . cprime)) (λ x10 . cprime)) (λ x9 . cprime)) (λ x8 . x2 x4))) ⟶ ∀ x3 x4 x5 x6 . wrex (λ x7 . wa (wbr (cv x7) (co (cdc c1 cc0) (cdc c2 c7) cexp) cle) (wral (λ x8 . wbr (cv x7) (cv x8) clt ⟶ wcel (cv x8) (x1 x3 x8 x4 x5 x6)) x2)) (λ x7 . cn)) ⟶ wrex (λ x1 . wrex (λ x2 . wa (w3a (wceq (cfv cc0 (cv x2)) c7) (wceq (cfv c1 (cv x2)) (cdc c1 c3)) (wceq (cfv (cv x1) (cv x2)) (co (cdc c8 c9) (co (cdc c1 cc0) (cdc c2 c9) cexp) cmul))) (wral (λ x3 . w3a (wcel (cfv (cv x3) (cv x2)) (cdif cprime (csn c2))) (wbr (co (cfv (co (cv x3) c1 caddc) (cv x2)) (cfv (cv x3) (cv x2)) cmin) (co (co c4 (co (cdc c1 cc0) (cdc c1 c8) cexp) cmul) c4 cmin) clt) (wbr c4 (co (cfv (co (cv x3) c1 caddc) (cv x2)) (cfv (cv x3) (cv x2)) cmin) clt)) (λ x3 . co cc0 (cv x1) cfzo))) (λ x2 . cfv (cv x1) ciccp)) (λ x1 . cfv c3 cuz) ⟶ (∀ x1 : ι → ο . w3a (wcel x1 ceven) (wbr c4 x1 clt) (wbr x1 (co c4 (co c10 (cdc c1 c8) cexp) cmul) cle) ⟶ wcel x1 cgbe) ⟶ wrex (λ x1 . wrex (λ x2 . wa (w3a (wceq (cfv cc0 (cv x2)) c7) (wceq (cfv c1 (cv x2)) (cdc c1 c3)) (wceq (cfv (cv x1) (cv x2)) (co (cdc c8 c9) (co c10 (cdc c2 c9) cexp) cmul))) (wral (λ x3 . w3a (wcel (cfv (cv x3) (cv x2)) (cdif cprime (csn c2))) (wbr (co (cfv (co (cv x3) c1 caddc) (cv x2)) (cfv (cv x3) (cv x2)) cmin) (co (co c4 (co c10 (cdc c1 c8) cexp) cmul) c4 cmin) clt) (wbr c4 (co (cfv (co (cv x3) c1 caddc) (cv x2)) (cfv (cv x3) (cv x2)) cmin) clt)) (λ x3 . co cc0 (cv x1) cfzo))) (λ x2 . cfv (cv x1) ciccp)) (λ x1 . cfv c3 cuz) ⟶ wrex (λ x1 . wa (wbr (cv x1) (co c10 (cdc c2 c7) cexp) cle) (wral (λ x2 . wbr (cv x1) (cv x2) clt ⟶ wcel (cv x2) cgbo) (λ x2 . codd))) (λ x1 . cn) ⟶ wceq cupwlks (cmpt (λ x1 . cvv) (λ x1 . copab (λ x2 x3 . w3a (wcel (cv x2) (cword (cdm (cfv (cv x1) ciedg)))) (wf (co cc0 (cfv (cv x2) chash) cfz) (cfv (cv x1) cvtx) (cv x3)) (wral (λ x4 . wceq (cfv (cfv (cv x4) (cv x2)) (cfv (cv x1) ciedg)) (cpr (cfv (cv x4) (cv x3)) (cfv (co (cv x4) c1 caddc) (cv x3)))) (λ x4 . co cc0 (cfv (cv x2) chash) cfzo))))) ⟶ wceq cspr (cmpt (λ x1 . cvv) (λ x1 . cab (λ x2 . wrex (λ x3 . wrex (λ x4 . wceq (cv x2) (cpr (cv x3) (cv x4))) (λ x4 . cv x1)) (λ x3 . cv x1)))) ⟶ wceq cmgmhm (cmpt2 (λ x1 x2 . cmgm) (λ x1 x2 . cmgm) (λ x1 x2 . crab (λ x3 . wral (λ x4 . wral (λ x5 . wceq (cfv (co (cv x4) (cv x5) (cfv (cv x1) cplusg)) (cv x3)) (co (cfv (cv x4) (cv x3)) (cfv (cv x5) (cv x3)) (cfv (cv x2) cplusg))) (λ x5 . cfv (cv x1) cbs)) (λ x4 . cfv (cv x1) cbs)) (λ x3 . co (cfv (cv x2) cbs) (cfv (cv x1) cbs) cmap))) ⟶ wceq csubmgm (cmpt (λ x1 . cmgm) (λ x1 . crab (λ x2 . wral (λ x3 . wral (λ x4 . wcel (co (cv x3) (cv x4) (cfv (cv x1) cplusg)) (cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2)) (λ x2 . cpw (cfv (cv x1) cbs)))) ⟶ wceq ccllaw (copab (λ x1 x2 . wral (λ x3 . wral (λ x4 . wcel (co (cv x3) (cv x4) (cv x1)) (cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2))) ⟶ wceq ccomlaw (copab (λ x1 x2 . wral (λ x3 . wral (λ x4 . wceq (co (cv x3) (cv x4) (cv x1)) (co (cv x4) (cv x3) (cv x1))) (λ x4 . cv x2)) (λ x3 . cv x2))) ⟶ wceq casslaw (copab (λ x1 x2 . wral (λ x3 . wral (λ x4 . wral (λ x5 . wceq (co (co (cv x3) (cv x4) (cv x1)) (cv x5) (cv x1)) (co (cv x3) (co (cv x4) (cv x5) (cv x1)) (cv x1))) (λ x5 . cv x2)) (λ x4 . cv x2)) (λ x3 . cv x2))) ⟶ wceq cintop (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . co (cv x2) (cxp (cv x1) (cv x1)) cmap)) ⟶ wceq cclintop (cmpt (λ x1 . cvv) (λ x1 . co (cv x1) (cv x1) cintop)) ⟶ wceq cassintop (cmpt (λ x1 . cvv) (λ x1 . crab (λ x2 . wbr (cv x2) (cv x1) casslaw) (λ x2 . cfv (cv x1) cclintop))) ⟶ x0) ⟶ x0
Axiom df_mgm2__df_cmgm2__df_sgrp2__df_csgrp2__df_rng0__df_rnghomo__df_rngisom__df_rngc__df_rngcALTV__df_ringc__df_ringcALTV__df_dmatalt__df_scmatalt__df_linc__df_lco__df_lininds__df_lindeps__df_fdiv : ∀ x0 : ο . (wceq cmgm2 (cab (λ x1 . wbr (cfv (cv x1) cplusg) (cfv (cv x1) cbs) ccllaw)) ⟶ wceq ccmgm2 (crab (λ x1 . wbr (cfv (cv x1) cplusg) (cfv (cv x1) cbs) ccomlaw) (λ x1 . cmgm2)) ⟶ wceq csgrp2 (crab (λ x1 . wbr (cfv (cv x1) cplusg) (cfv (cv x1) cbs) casslaw) (λ x1 . cmgm2)) ⟶ wceq ccsgrp2 (crab (λ x1 . wbr (cfv (cv x1) cplusg) (cfv (cv x1) cbs) ccomlaw) (λ x1 . csgrp2)) ⟶ wceq crng (crab (λ x1 . wa (wcel (cfv (cv x1) cmgp) csgrp) (wsbc (λ x2 . wsbc (λ x3 . wsbc (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wa (wceq (co (cv x5) (co (cv x6) (cv x7) (cv x3)) (cv x4)) (co (co (cv x5) (cv x6) (cv x4)) (co (cv x5) (cv x7) (cv x4)) (cv x3))) (wceq (co (co (cv x5) (cv x6) (cv x3)) (cv x7) (cv x4)) (co (co (cv x5) (cv x7) (cv x4)) (co (cv x6) (cv x7) (cv x4)) (cv x3)))) (λ x7 . cv x2)) (λ x6 . cv x2)) (λ x5 . cv x2)) (cfv (cv x1) cmulr)) (cfv (cv x1) cplusg)) (cfv (cv x1) cbs))) (λ x1 . cabl)) ⟶ wceq crngh (cmpt2 (λ x1 x2 . crng) (λ x1 x2 . crng) (λ x1 x2 . csb (cfv (cv x1) cbs) (λ x3 . csb (cfv (cv x2) cbs) (λ x4 . crab (λ x5 . wral (λ x6 . wral (λ x7 . wa (wceq (cfv (co (cv x6) (cv x7) (cfv (cv x1) cplusg)) (cv x5)) (co (cfv (cv x6) (cv x5)) (cfv (cv x7) (cv x5)) (cfv (cv x2) cplusg))) (wceq (cfv (co (cv x6) (cv x7) (cfv (cv x1) cmulr)) (cv x5)) (co (cfv (cv x6) (cv x5)) (cfv (cv x7) (cv x5)) (cfv (cv x2) cmulr)))) (λ x7 . cv x3)) (λ x6 . cv x3)) (λ x5 . co (cv x4) (cv x3) cmap))))) ⟶ wceq crngs (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . crab (λ x3 . wcel (ccnv (cv x3)) (co (cv x2) (cv x1) crngh)) (λ x3 . co (cv x1) (cv x2) crngh))) ⟶ wceq crngc (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cv x1) cestrc) (cres crngh (cxp (cin (cv x1) crng) (cin (cv x1) crng))) cresc)) ⟶ wceq crngcALTV (cmpt (λ x1 . cvv) (λ x1 . csb (cin (cv x1) crng) (λ x2 . ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx chom) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . co (cv x3) (cv x4) crngh))) (cop (cfv cnx cco) (cmpt2 (λ x3 x4 . cxp (cv x2) (cv x2)) (λ x3 x4 . cv x2) (λ x3 x4 . cmpt2 (λ x5 x6 . co (cfv (cv x3) c2nd) (cv x4) crngh) (λ x5 x6 . co (cfv (cv x3) c1st) (cfv (cv x3) c2nd) crngh) (λ x5 x6 . ccom (cv x5) (cv x6)))))))) ⟶ wceq cringc (cmpt (λ x1 . cvv) (λ x1 . co (cfv (cv x1) cestrc) (cres crh (cxp (cin (cv x1) crg) (cin (cv x1) crg))) cresc)) ⟶ wceq cringcALTV (cmpt (λ x1 . cvv) (λ x1 . csb (cin (cv x1) crg) (λ x2 . ctp (cop (cfv cnx cbs) (cv x2)) (cop (cfv cnx chom) (cmpt2 (λ x3 x4 . cv x2) (λ x3 x4 . cv x2) (λ x3 x4 . co (cv x3) (cv x4) crh))) (cop (cfv cnx cco) (cmpt2 (λ x3 x4 . cxp (cv x2) (cv x2)) (λ x3 x4 . cv x2) (λ x3 x4 . cmpt2 (λ x5 x6 . co (cfv (cv x3) c2nd) (cv x4) crh) (λ x5 x6 . co (cfv (cv x3) c1st) (cfv (cv x3) c2nd) crh) (λ x5 x6 . ccom (cv x5) (cv x6)))))))) ⟶ wceq cdmatalt (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . csb (co (cv x1) (cv x2) cmat) (λ x3 . co (cv x3) (crab (λ x4 . wral (λ x5 . wral (λ x6 . wne (cv x5) (cv x6) ⟶ wceq (co (cv x5) (cv x6) (cv x4)) (cfv (cv x2) c0g)) (λ x6 . cv x1)) (λ x5 . cv x1)) (λ x4 . cfv (cv x3) cbs)) cress))) ⟶ wceq cscmatalt (cmpt2 (λ x1 x2 . cfn) (λ x1 x2 . cvv) (λ x1 x2 . csb (co (cv x1) (cv x2) cmat) (λ x3 . co (cv x3) (crab (λ x4 . wrex (λ x5 . wral (λ x6 . wral (λ x7 . wceq (co (cv x6) (cv x7) (cv x4)) (cif (wceq (cv x6) (cv x7)) (cv x5) (cfv (cv x2) c0g))) (λ x7 . cv x1)) (λ x6 . cv x1)) (λ x5 . cfv (cv x2) cbs)) (λ x4 . cfv (cv x3) cbs)) cress))) ⟶ wceq clinc (cmpt (λ x1 . cvv) (λ x1 . cmpt2 (λ x2 x3 . co (cfv (cfv (cv x1) csca) cbs) (cv x3) cmap) (λ x2 x3 . cpw (cfv (cv x1) cbs)) (λ x2 x3 . co (cv x1) (cmpt (λ x4 . cv x3) (λ x4 . co (cfv (cv x4) (cv x2)) (cv x4) (cfv (cv x1) cvsca))) cgsu))) ⟶ wceq clinco (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cpw (cfv (cv x1) cbs)) (λ x1 x2 . crab (λ x3 . wrex (λ x4 . wa (wbr (cv x4) (cfv (cfv (cv x1) csca) c0g) cfsupp) (wceq (cv x3) (co (cv x4) (cv x2) (cfv (cv x1) clinc)))) (λ x4 . co (cfv (cfv (cv x1) csca) cbs) (cv x2) cmap)) (λ x3 . cfv (cv x1) cbs))) ⟶ wceq clininds (copab (λ x1 x2 . wa (wcel (cv x1) (cpw (cfv (cv x2) cbs))) (wral (λ x3 . wa (wbr (cv x3) (cfv (cfv (cv x2) csca) c0g) cfsupp) (wceq (co (cv x3) (cv x1) (cfv (cv x2) clinc)) (cfv (cv x2) c0g)) ⟶ wral (λ x4 . wceq (cfv (cv x4) (cv x3)) (cfv (cfv (cv x2) csca) c0g)) (λ x4 . cv x1)) (λ x3 . co (cfv (cfv (cv x2) csca) cbs) (cv x1) cmap)))) ⟶ wceq clindeps (copab (λ x1 x2 . wn (wbr (cv x1) (cv x2) clininds))) ⟶ wceq cfdiv (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cres (co (cv x1) (cv x2) (cof cdiv)) (co (cv x2) cc0 csupp))) ⟶ x0) ⟶ x0
Axiom df_bigo__df_blen__df_dig__df_setrecs__df_pg__df_gte__df_gt__df_sinh__df_cosh__df_tanh__df_sec__df_csc__df_cot__df_logbALT__df_reflexive__df_irreflexive__df_alsi__df_alsc : ∀ x0 : ο . (wceq cbigo (cmpt (λ x1 . co cr cr cpm) (λ x1 . crab (λ x2 . wrex (λ x3 . wrex (λ x4 . wral (λ x5 . wbr (cfv (cv x5) (cv x2)) (co (cv x4) (cfv (cv x5) (cv x1)) cmul) cle) (λ x5 . cin (cdm (cv x2)) (co (cv x3) cpnf cico))) (λ x4 . cr)) (λ x3 . cr)) (λ x2 . co cr cr cpm))) ⟶ wceq cblen (cmpt (λ x1 . cvv) (λ x1 . cif (wceq (cv x1) cc0) c1 (co (cfv (co c2 (cfv (cv x1) cabs) clogb) cfl) c1 caddc))) ⟶ wceq cdig (cmpt (λ x1 . cn) (λ x1 . cmpt2 (λ x2 x3 . cz) (λ x2 x3 . co cc0 cpnf cico) (λ x2 x3 . co (cfv (co (co (cv x1) (cneg (cv x2)) cexp) (cv x3) cmul) cfl) (cv x1) cmo))) ⟶ (∀ x1 : ι → ο . wceq (csetrecs x1) (cuni (cab (λ x2 . ∀ x3 . (∀ x4 . wss (cv x4) (cv x2) ⟶ wss (cv x4) (cv x3) ⟶ wss (cfv (cv x4) x1) (cv x3)) ⟶ wss (cv x2) (cv x3))))) ⟶ wceq cpg (csetrecs (cmpt (λ x1 . cvv) (λ x1 . cxp (cpw (cv x1)) (cpw (cv x1))))) ⟶ wceq cge_real (ccnv cle) ⟶ wceq cgt (ccnv clt) ⟶ wceq csinh (cmpt (λ x1 . cc) (λ x1 . co (cfv (co ci (cv x1) cmul) csin) ci cdiv)) ⟶ wceq ccosh (cmpt (λ x1 . cc) (λ x1 . cfv (co ci (cv x1) cmul) ccos)) ⟶ wceq ctanh (cmpt (λ x1 . cima (ccnv ccosh) (cdif cc (csn cc0))) (λ x1 . co (cfv (co ci (cv x1) cmul) ctan) ci cdiv)) ⟶ wceq csec (cmpt (λ x1 . crab (λ x2 . wne (cfv (cv x2) ccos) cc0) (λ x2 . cc)) (λ x1 . co c1 (cfv (cv x1) ccos) cdiv)) ⟶ wceq ccsc (cmpt (λ x1 . crab (λ x2 . wne (cfv (cv x2) csin) cc0) (λ x2 . cc)) (λ x1 . co c1 (cfv (cv x1) csin) cdiv)) ⟶ wceq ccot (cmpt (λ x1 . crab (λ x2 . wne (cfv (cv x2) csin) cc0) (λ x2 . cc)) (λ x1 . co (cfv (cv x1) ccos) (cfv (cv x1) csin) cdiv)) ⟶ wceq clog_ (cmpt (λ x1 . cdif cc (cpr cc0 c1)) (λ x1 . cmpt (λ x2 . cdif cc (csn cc0)) (λ x2 . co (cfv (cv x2) clog) (cfv (cv x1) clog) cdiv))) ⟶ (∀ x1 x2 : ι → ο . wb (wreflexive x1 x2) (wa (wss x2 (cxp x1 x1)) (wral (λ x3 . wbr (cv x3) (cv x3) x2) (λ x3 . x1)))) ⟶ (∀ x1 x2 : ι → ο . wb (wirreflexive x1 x2) (wa (wss x2 (cxp x1 x1)) (wral (λ x3 . wn (wbr (cv x3) (cv x3) x2)) (λ x3 . x1)))) ⟶ (∀ x1 x2 : ι → ο . wb (walsi x1 x2) (wa (∀ x3 . x1 x3 ⟶ x2 x3) (wex x1))) ⟶ (∀ x1 : ι → ο . ∀ x2 : ι → ι → ο . wb (walsc x1 x2) (wa (wral x1 x2) (wex (λ x3 . wcel (cv x3) (x2 x3))))) ⟶ x0) ⟶ x0