Let x0 of type ι be given.

Let x1 of type ι → ι be given.

Let x2 of type ι → ι be given.

Assume H0: ∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3.

Claim L1: 0fc90.. x0 x1 = 0fc90.. x0 x2

Apply unknownprop_075a71193d04eff3936ee7246a228619e3dbe0ea2b9d96d40e9b467470ee4a92 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 (0fc90.. x0 x1)) = 0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x5 . If_i (x5 = 4a7ef..) x0 x3).

Let x3 of type ι → ι → ο be given.

Assume H2: x3 (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (0fc90.. x0 x1))) (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (0fc90.. x0 x1))).

The subproof is completed by applying H2.

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Proofgold Proof