Let x0 of type ι be given.

Let x1 of type (ι → ο) → ο be given.

Let x2 of type (ι → ο) → ο be given.

Let x3 of type ι → ι be given.

Let x4 of type ι → ι be given.

Assume H0: ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ iff (x1 x5) (x2 x5).

Assume H1: ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = x4 x5.

Claim L2: e0e40.. x0 x1 = e0e40.. x0 x2

Apply unknownprop_35ee954b0de81ace4d484d57278ef6dea3fd2cb486e752fb5784dfc8cd9b7c4a with x0, x1, x2.

The subproof is completed by applying H0.

Claim L3: 0fc90.. x0 x3 = 0fc90.. x0 x4

Apply unknownprop_075a71193d04eff3936ee7246a228619e3dbe0ea2b9d96d40e9b467470ee4a92 with x0, x3, x4.

The subproof is completed by applying H1.

Let x5 of type ι → ι → ο be given.

The subproof is completed by applying H4.

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Proofgold Proof