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Proofgold Proposition

∀ 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
type
prop
theory
SetMM
name
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
proof
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proofgold address
TMUKs..
creator
36224 PrCmT../fdb98..
owner
36224 PrCmT../fdb98..
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0891a..