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Proofgold Proof

pf
Apply 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 with wceq cstrkgb (cab (λ x0 . wsbc (λ x1 . wsbc (λ x2 . w3a (wral (λ x3 . wral (λ x4 . wcel (cv x4) (co (cv x3) (cv x3) (cv x2))wceq (cv x3) (cv x4)) (λ x4 . cv x1)) (λ x3 . cv x1)) (wral (λ x3 . wral (λ x4 . wral (λ x5 . wral (λ x6 . wral (λ x7 . wa (wcel (cv x6) (co (cv x3) (cv x5) (cv x2))) (wcel (cv x7) (co (cv x4) (cv x5) (cv x2)))wrex (λ x8 . wa (wcel (cv x8) (co (cv x6) (cv x4) (cv x2))) (wcel (cv x8) (co (cv x7) (cv x3) (cv x2)))) (λ x8 . cv x1)) (λ x7 . cv x1)) (λ x6 . cv x1)) (λ x5 . cv x1)) (λ x4 . cv x1)) (λ x3 . cv x1)) (wral (λ x3 . wral (λ x4 . wrex (λ x5 . wral (λ x6 . wral (λ x7 . wcel (cv x6) (co (cv x5) (cv x7) (cv x2))) (λ x7 . cv x4)) (λ x6 . cv x3)) (λ x5 . cv x1)wrex (λ x5 . wral (λ x6 . wral (λ x7 . wcel (cv x5) (co (cv x6) (cv x7) (cv x2))) (λ x7 . cv x4)) (λ x6 . cv x3)) (λ x5 . cv x1)) (λ x4 . cpw (cv x1))) (λ x3 . cpw (cv x1)))) (cfv (cv x0) citv)) (cfv (cv x0) cbs))).
Assume H0: wceq cppi (cmpt (λ x0 . cr) (λ x0 . cfv (cin (co cc0 (cv x0) cicc) cprime) chash)).
Assume H1: wceq cmu (cmpt (λ x0 . cn) (λ x0 . cif (wrex (λ x1 . wbr (co (cv x1) c2 cexp) (cv x0) cdvds) (λ x1 . cprime)) cc0 (co (cneg c1) (cfv (crab (λ x1 . wbr (cv x1) (cv x0) cdvds) (λ x1 . cprime)) chash) cexp))).
Assume H2: wceq csgm (cmpt2 (λ x0 x1 . cc) (λ x0 x1 . cn) (λ x0 x1 . csu (crab (λ x2 . wbr (cv x2) (cv x1) cdvds) (λ x2 . cn)) (λ x2 . co (cv ...) ... ...))).
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