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Proofgold Proof

pf
Apply unknownprop_f04ee3f2db7dade92ee7be101bff40fb89f733bb0c0340f09b616cd72154ad93 with λ x0 . bc82c.. (f4dc0.. x0) x0 = 4a7ef...
Let x0 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: ∀ x1 . prim1 x1 (56ded.. (e4431.. x0)) ⟶ bc82c.. (f4dc0.. x1) x1 = 4a7ef...
Claim L2: ...
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Apply unknownprop_b2d3cb96a6a882d02e5e57dcfc02559b580d1f8621959f82afe70dc68a4b010f with f4dc0.. x0, x0, λ x1 x2 . x2 = 4a7ef.. leaving 3 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying H0.
Claim L3: ...
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Claim L4: ...
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Claim L5: ...
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Apply L5 with 02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) = 4a7ef...
Assume H6: Subq (e4431.. (02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))))) (e4431.. 4a7ef..).
Assume H7: SNoEq_ (e4431.. (02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))))) (02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1)))) 4a7ef...
Apply unknownprop_c3102c186c7aa1001a5c1b1b7ecab6b25bcd639e713104221ece8bf414726a69 with 02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))), 4a7ef.. leaving 4 subgoals.
The subproof is completed by applying L4.
The subproof is completed by applying unknownprop_a66a65189a5389c2141d18df52f52fcf5f074fba68040a0bda3b8b81c830611a.
Apply set_ext with e4431.. (02a50.. (0ac37.. (94f9e.. (23e07.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (23e07.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1))) (0ac37.. (94f9e.. (5246e.. (f4dc0.. x0)) (λ x1 . bc82c.. x1 x0)) (94f9e.. (5246e.. x0) (λ x1 . bc82c.. (f4dc0.. x0) x1)))), ... leaving 2 subgoals.
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