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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 236dc.. x0 x1 = 236dc.. x2 x3.
Let x4 of type ι be given.
Assume H2: prim1 x4 x0.
Claim L3: prim1 x4 (236dc.. x2 x3)
Apply H1 with λ x5 x6 . prim1 x4 x5.
Apply unknownprop_0b5b61a66a1ed2eb843dbce5c5f6930c63a284fe5e33704d9f0cc564310ec40b with x0, 94f9e.. x1 (λ x5 . (λ x6 . 15418.. x6 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5), x4.
The subproof is completed by applying H2.
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x2, 94f9e.. x3 (λ x5 . (λ x6 . 15418.. x6 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5), x4, prim1 x4 x2 leaving 3 subgoals.
The subproof is completed by applying L3.
Assume H4: prim1 x4 x2.
The subproof is completed by applying H4.
Assume H4: prim1 x4 (94f9e.. x3 (λ x5 . (λ x6 . 15418.. x6 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5)).
Apply FalseE with prim1 x4 x2.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with x3, λ x5 . (λ x6 . 15418.. x6 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5, x4, False leaving 2 subgoals.
The subproof is completed by applying H4.
Let x5 of type ι be given.
Assume H5: prim1 x5 x3.
Assume H6: x4 = (λ x6 . 15418.. x6 (91630.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5.
Apply unknownprop_4248039866c31bbba3c8ed2d0af8ec07d1aa91eb2387bfc31d9d9cb3da47787a with x0, x5 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H6 with λ x6 x7 . prim1 x6 x0.
The subproof is completed by applying H2.
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