Let x0 of type ι be given.

Let x1 of type ι → ι → ο be given.

Let x2 of type ι → ι → ο be given.

Assume H0: ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ iff (x1 x3 x4) (x2 x3 x4).

Claim L1: d2155.. x0 x1 = d2155.. x0 x2

Apply unknownprop_75d5b46497f20dc30e2e5351a60197c4fa9d445bc23c6c8245597bb858180907 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 (d2155.. 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 (d2155.. x0 x2))) (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (d2155.. x0 x2))).

The subproof is completed by applying H2.

■

Proofgold Proof