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Proofgold Proof

pf
Apply unknownprop_98dce570015dab8b9107dc33a5e2e4ea0417c490e1cfe00b91b6267d26e82089 with λ x0 x1 . Subq (e4431.. (bc82c.. x0 x1)) (bc82c.. (e4431.. x0) (e4431.. x1)).
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Claim L2: ...
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Claim L3: ...
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Assume H4: ∀ x2 . prim1 x2 (56ded.. (e4431.. x0)) ⟶ (λ x3 x4 . Subq (e4431.. (bc82c.. x3 x4)) (bc82c.. (e4431.. x3) (e4431.. x4))) x2 x1.
Assume H5: ∀ x2 . prim1 x2 (56ded.. (e4431.. x1)) ⟶ (λ x3 x4 . Subq (e4431.. (bc82c.. x3 x4)) (bc82c.. (e4431.. x3) (e4431.. x4))) x0 x2.
Assume H6: ∀ x2 . prim1 x2 (56ded.. (e4431.. x0)) ⟶ ∀ x3 . prim1 x3 (56ded.. (e4431.. x1)) ⟶ (λ x4 x5 . Subq (e4431.. (bc82c.. x4 x5)) (bc82c.. (e4431.. x4) (e4431.. x5))) x2 x3.
Apply unknownprop_b2d3cb96a6a882d02e5e57dcfc02559b580d1f8621959f82afe70dc68a4b010f with x0, x1, λ x2 x3 . Subq (e4431.. x3) (bc82c.. (e4431.. x0) (e4431.. x1)) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Claim L7: ...
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Apply unknownprop_b01da77c5200afb1f524e6033a58358c3303b7f4989ae9962b195b5bb398525b with 0ac37.. (94f9e.. (23e07.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (23e07.. x1) (λ x2 . bc82c.. x0 x2)), 0ac37.. (94f9e.. (5246e.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (5246e.. x1) (λ x2 . bc82c.. x0 x2)), Subq (e4431.. (02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (23e07.. x1) (λ x2 . bc82c.. x0 x2))) (0ac37.. (94f9e.. (5246e.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (5246e.. x1) (λ x2 . bc82c.. x0 x2))))) (bc82c.. (e4431.. x0) (e4431.. x1)) leaving 2 subgoals.
The subproof is completed by applying L7.
Assume H8: 80242.. (02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (23e07.. x1) (λ x2 . bc82c.. x0 x2))) (0ac37.. (94f9e.. (5246e.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (5246e.. x1) (λ x2 . bc82c.. x0 x2)))).
Assume H9: prim1 (e4431.. (02a50.. (0ac37.. (94f9e.. (23e07.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (23e07.. x1) (λ x2 . bc82c.. x0 x2))) (0ac37.. (94f9e.. (5246e.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (5246e.. x1) (λ x2 . bc82c.. x0 x2))))) (4ae4a.. (0ac37.. (a842e.. (0ac37.. (94f9e.. (23e07.. x0) (λ x2 . bc82c.. x2 x1)) (94f9e.. (23e07.. x1) (λ x2 . bc82c.. x0 x2))) (λ x2 . 4ae4a.. (e4431.. x2))) (a842e.. (0ac37.. ... ...) ...))).
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