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Proofgold Proof

pf
Apply 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 with wceq com (crab (λ x0 . ∀ x1 . wlim (cv x1)wcel (cv x0) (cv x1)) (λ x0 . con0)).
Assume H0: ∀ x0 x1 : ι → ο . wb (wfn x0 x1) (wa (wfun x0) (wceq (cdm x0) x1)).
Assume H1: ∀ x0 x1 x2 : ι → ο . wb (wf x0 x1 x2) (wa (wfn x2 x0) (wss (crn x2) x1)).
Assume H2: ∀ x0 x1 x2 : ι → ο . wb (wf1 x0 x1 x2) (wa (wf x0 x1 x2) (wfun (ccnv x2))).
Assume H3: ∀ x0 x1 x2 : ι → ο . wb (wfo x0 x1 x2) (wa (wfn x2 x0) (wceq (crn x2) x1)).
Assume H4: ∀ x0 x1 x2 : ι → ο . wb (wf1o x0 x1 x2) (wa (wf1 x0 x1 x2) (wfo x0 x1 x2)).
Assume H5: ∀ x0 x1 : ι → ο . wceq (cfv x0 x1) (cio (λ x2 . wbr x0 (cv x2) x1)).
Assume H6: ∀ x0 x1 x2 x3 x4 : ι → ο . wb (wiso x0 x1 x2 x3 x4) (wa (wf1o x0 x1 x4) (wral (λ x5 . wral (λ x6 . wb (wbr (cv x5) (cv x6) x2) (wbr (cfv (cv x5) x4) (cfv (cv x6) x4) x3)) (λ x6 . x0)) (λ x5 . x0))).
Assume H7: ∀ x0 : ι → ο . ∀ x1 : ι → ι → ο . wceq (crio (λ x2 . x0 x2) (λ x2 . x1 x2)) (cio (λ x2 . wa (wcel (cv x2) (x1 x2)) (x0 x2))).
Assume H8: ∀ x0 x1 x2 : ι → ο . wceq (co x0 x1 x2) (cfv (cop x0 x1) x2).
Assume H9: ∀ x0 : ι → ι → ι → ο . wceq (coprab (λ x1 x2 x3 . x0 x1 x2 x3)) (cab (λ x1 . wex (λ x2 . wex (λ x3 . wex (λ x4 . wa (wceq (cv x1) (cop (cop (cv x2) (cv x3)) (cv x4))) (x0 x2 x3 x4)))))).
Assume H10: ∀ x0 x1 x2 : ι → ι → ι → ο . wceq (cmpt2 (λ x3 x4 . x0 x3 x4) (λ x3 x4 . x1 x3 x4) (λ x3 x4 . x2 x3 x4)) (coprab (λ x3 x4 x5 . wa (wa (wcel (cv x3) (x0 x3 x4)) (wcel (cv x4) (x1 x3 x4))) (wceq (cv x5) (x2 x3 x4)))).
Assume H11: ∀ x0 : ι → ο . wceq (cof x0) (cmpt2 (λ x1 x2 . cvv) (λ x1 x2 . cvv) (λ x1 x2 . cmpt ... ...)).
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