Let x0 of type ι be given.

Let x1 of type ι → ο be given.

Let x2 of type ι → ο be given.

Assume H0: ∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3).

Claim L1: 1216a.. x0 x1 = 1216a.. x0 x2

Apply unknownprop_b3f0546588eaaffbfada457a1b6c239e49888b4c546cfd7ac96a6a43fd9db95e with x0, x1, x2.

The subproof is completed by applying H0.

Apply L1 with λ x3 x4 . 0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x5 . If_i (x5 = 4a7ef..) x0 x4) = 0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x5 . If_i (x5 = 4a7ef..) x0 (1216a.. x0 x2)).

Let x3 of type ι → ι → ο be given.

Assume H2: x3 (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (1216a.. x0 x2))) (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (1216a.. x0 x2))).

The subproof is completed by applying H2.

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Proofgold Proof