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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: Subq x0 x1.
Let x2 of type ι be given.
Assume H1: prim1 x2 (0ac37.. x0 (94f9e.. x0 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3))).
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with x0, 94f9e.. x0 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2, prim1 x2 (472ec.. x1) leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H2: prim1 x2 x0.
Apply unknownprop_0b5b61a66a1ed2eb843dbce5c5f6930c63a284fe5e33704d9f0cc564310ec40b with x1, 94f9e.. x1 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2.
Apply H0 with x2.
The subproof is completed by applying H2.
Assume H2: prim1 x2 (94f9e.. x0 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3)).
Apply unknownprop_e4d6e0bfb4ef6d52ee13edd54a77c8cc7f0a3af8ffb1b8da66d4f98842dd28b5 with x1, 94f9e.. x1 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3), x2.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with x0, λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3, x2, prim1 x2 (94f9e.. x1 (λ x3 . (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3)) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H3: prim1 x3 x0.
Assume H4: x2 = (λ x4 . 15418.. x4 (91630.. (4ae4a.. 4a7ef..))) x3.
Apply H4 with λ x4 x5 . prim1 x5 (94f9e.. x1 (λ x6 . (λ x7 . 15418.. x7 (91630.. (4ae4a.. 4a7ef..))) x6)).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with x1, λ x4 . (λ x5 . 15418.. x5 (91630.. (4ae4a.. 4a7ef..))) x4, x3.
Apply H0 with x3.
The subproof is completed by applying H3.
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