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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Assume H0: prim1 x2 (0fc90.. x0 (λ x3 . x1 x3)).
Claim L1: ∃ x3 . and (prim1 x3 x0) (prim1 x2 (94f9e.. (x1 x3) (λ x4 . aae7a.. x3 x4)))
Apply unknownprop_6e713ef2b1c9d2089dead8e3d98fed6bda91ffc6b807ed8732c89724a15f5c2c with x0, λ x3 . 94f9e.. (x1 x3) (λ x4 . aae7a.. x3 x4), x2.
The subproof is completed by applying H0.
Apply exandE_i with λ x3 . prim1 x3 x0, λ x3 . prim1 x2 (94f9e.. (x1 x3) (λ x4 . aae7a.. x3 x4)), and (and (aae7a.. (e76d4.. x2) (22ca9.. x2) = x2) (prim1 (e76d4.. x2) x0)) (prim1 (22ca9.. x2) (x1 (e76d4.. x2))) leaving 2 subgoals.
The subproof is completed by applying L1.
Let x3 of type ι be given.
Assume H2: prim1 x3 x0.
Assume H3: prim1 x2 (94f9e.. (x1 x3) (λ x4 . aae7a.. x3 x4)).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with x1 x3, aae7a.. x3, x2, and (and (aae7a.. (e76d4.. x2) (22ca9.. x2) = x2) (prim1 (e76d4.. x2) x0)) (prim1 (22ca9.. x2) (x1 (e76d4.. x2))) leaving 2 subgoals.
The subproof is completed by applying H3.
Let x4 of type ι be given.
Assume H4: prim1 x4 (x1 x3).
Assume H5: x2 = aae7a.. x3 x4.
Apply H5 with λ x5 x6 . and (and (aae7a.. (e76d4.. x6) (22ca9.. x6) = x6) (prim1 (e76d4.. x6) x0)) (prim1 (22ca9.. x6) (x1 (e76d4.. x6))).
Apply unknownprop_7e986439242ce85fa04e4b7be2035418e9dbee6641ed66c6c5b7be52a2254fca with x3, x4, λ x5 x6 . and (and (aae7a.. x6 (22ca9.. (aae7a.. x3 x4)) = aae7a.. x3 x4) (prim1 x6 x0)) (prim1 (22ca9.. (aae7a.. x3 x4)) (x1 x6)).
Apply unknownprop_916f469d850241375b1e44b2c6308f0113078869ceee129c02712fae69c32a37 with x3, x4, λ x5 x6 . and (and (aae7a.. x3 x6 = aae7a.. x3 x4) (prim1 x3 x0)) (prim1 x6 (x1 x3)).
Apply and3I with aae7a.. x3 x4 = aae7a.. x3 x4, prim1 x3 x0, prim1 x4 (x1 x3) leaving 3 subgoals.
Let x5 of type ι → ι → ο be given.
Assume H6: x5 (aae7a.. x3 x4) (aae7a.. x3 x4).
The subproof is completed by applying H6.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
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