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Proofgold Proof

pf
Let x0 of type ιι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply set_ext with 94f9e.. (prim2 x1 x2) (λ x3 . x0 x3), prim2 (x0 x1) (x0 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: prim1 x3 (94f9e.. (prim2 x1 x2) (λ x4 . x0 x4)).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with prim2 x1 x2, x0, x3, prim1 x3 (prim2 (x0 x1) (x0 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x4 of type ι be given.
Assume H1: prim1 x4 (prim2 x1 x2).
Assume H2: x3 = x0 x4.
Apply H2 with λ x5 x6 . prim1 x6 (prim2 (x0 x1) (x0 x2)).
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with x4, x1, x2, prim1 (x0 x4) (prim2 (x0 x1) (x0 x2)) leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H3: x4 = x1.
Apply H3 with λ x5 x6 . prim1 (x0 x6) (prim2 (x0 x1) (x0 x2)).
The subproof is completed by applying unknownprop_893870ab8a49d622c10a8fe954eea30d7bd2b94aa27e9c6b21eab85a9f81d115 with x0 x1, x0 x2.
Assume H3: x4 = x2.
Apply H3 with λ x5 x6 . prim1 (x0 x6) (prim2 (x0 x1) (x0 x2)).
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x0 x1, x0 x2.
Let x3 of type ι be given.
Assume H0: prim1 x3 (prim2 (x0 x1) (x0 x2)).
Apply unknownprop_44132e34b8fcc92e54ff875d0e8f6137eeea7d41bb9d4b117dbbbb4d2f239782 with x3, x0 x1, x0 x2, prim1 x3 (94f9e.. (prim2 x1 x2) (λ x4 . x0 x4)) leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: x3 = x0 x1.
Apply H1 with λ x4 x5 . prim1 x5 (94f9e.. (prim2 x1 x2) (λ x6 . x0 x6)).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with prim2 x1 x2, x0, x1.
The subproof is completed by applying unknownprop_893870ab8a49d622c10a8fe954eea30d7bd2b94aa27e9c6b21eab85a9f81d115 with x1, x2.
Assume H1: x3 = x0 x2.
Apply H1 with λ x4 x5 . prim1 x5 (94f9e.. (prim2 x1 x2) (λ x6 . x0 x6)).
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with prim2 x1 x2, x0, x2.
The subproof is completed by applying unknownprop_70f06371245ce38fbbca963cb4d7e422ccf350d2e27735c617635b09cbcba701 with x1, x2.