Let x0 of type ι be given.

Let x1 of type ι → ι → ι be given.

Let x2 of type ι → ι → ι be given.

Assume H0: ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4.

Claim L1: eb53d.. x0 x1 = eb53d.. x0 x2

Apply unknownprop_dbb26cd650ab4f49eb7a56474ebdc3b4a46f79fd66ae7129c609d055a8e1a150 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 (eb53d.. 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 (eb53d.. x0 x1))) (0fc90.. (4ae4a.. (4ae4a.. 4a7ef..)) (λ x4 . If_i (x4 = 4a7ef..) x0 (eb53d.. x0 x1))).

The subproof is completed by applying H2.

■

Proofgold Proof