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Proofgold Proposition

∀ 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
type
prop
theory
SetMM
name
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
proof
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proofgold address
TMJnw..
creator
36224 PrCmT../f401b..
owner
36224 PrCmT../f401b..
term root
4196c..