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Proofgold Proof

pf
Apply unknownprop_98dce570015dab8b9107dc33a5e2e4ea0417c490e1cfe00b91b6267d26e82089 with λ x0 x1 . bc82c.. x0 x1 = bc82c.. x1 x0.
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: ∀ x2 . prim1 x2 (56ded.. (e4431.. x0)) ⟶ bc82c.. x2 x1 = bc82c.. x1 x2.
Assume H3: ∀ x2 . prim1 x2 (56ded.. (e4431.. x1)) ⟶ bc82c.. x0 x2 = bc82c.. x2 x0.
Assume H4: ∀ x2 . prim1 x2 (56ded.. (e4431.. x0)) ⟶ ∀ x3 . prim1 x3 (56ded.. (e4431.. x1)) ⟶ bc82c.. x2 x3 = bc82c.. x3 x2.
Claim L5: ...
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Claim L6: ...
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Claim L7: ...
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Claim L8: ...
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Apply unknownprop_b2d3cb96a6a882d02e5e57dcfc02559b580d1f8621959f82afe70dc68a4b010f with x0, x1, λ x2 x3 . x3 = bc82c.. x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_b2d3cb96a6a882d02e5e57dcfc02559b580d1f8621959f82afe70dc68a4b010f with x1, x0, λ x2 x3 . 02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x4 . bc82c.. x4 x1)) (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x0 x4))) (0ac37.. (94f9e.. (5246e.. x0) (λ x4 . bc82c.. x4 x1)) (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x0 x4))) = x3 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Claim L9: ...
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Claim L10: ...
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Claim L11: ...
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Claim L12: ...
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Apply L9 with λ x2 x3 . 02a50.. (0ac37.. x3 (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x0 x4))) (0ac37.. (94f9e.. (5246e.. x0) (λ x4 . bc82c.. x4 x1)) (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x0 x4))) = 02a50.. (0ac37.. (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x4 x0)) (94f9e.. (23e07.. x0) (λ x4 . bc82c.. x1 x4))) (0ac37.. (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x4 x0)) (94f9e.. (5246e.. x0) (λ x4 . bc82c.. x1 x4))).
Apply L10 with λ x2 x3 . 02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x4 . bc82c.. x1 x4)) x3) (0ac37.. (94f9e.. (5246e.. x0) (λ x4 . bc82c.. x4 x1)) (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x0 x4))) = 02a50.. (0ac37.. (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x4 x0)) (94f9e.. (23e07.. x0) (λ x4 . bc82c.. x1 x4))) (0ac37.. (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x4 x0)) (94f9e.. (5246e.. x0) (λ x4 . bc82c.. x1 x4))).
Apply L11 with λ x2 x3 . 02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x4 . bc82c.. x1 x4)) (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x4 x0))) (0ac37.. x3 (94f9e.. (5246e.. x1) (λ x4 . bc82c.. x0 x4))) = 02a50.. (0ac37.. (94f9e.. (23e07.. x1) (λ x4 . bc82c.. x4 ...)) ...) ....
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