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.

Let x3 of type ι be given.

Assume H0: ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = x2 x4 x5.

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 x4 x5 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) x3)) = 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x4 x3)).

Let x4 of type ι → ι → ο be given.

The subproof is completed by applying H2.

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Proofgold Proof