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Proofgold Proposition

∀ 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
type
prop
theory
SetMM
name
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
proof
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