Let x0 of type ι → (ι → ο) → ο be given.

Let x1 of type ι → (ι → ο) → ο be given.

Let x2 of type ι be given.

Assume H0: ordinal x2.

Let x3 of type ι → ο be given.

Let x4 of type ι → ο be given.

Assume H1: PNoEq_ x2 x3 x4.

Assume H2: 47618.. x0 x1 x2 x3.

Apply H2 with 47618.. x0 x1 x2 x4.

Assume H3: cae4c.. x0 x2 x3.

Assume H4: bc2b0.. x1 x2 x3.

Apply andI with cae4c.. x0 x2 x4, bc2b0.. x1 x2 x4 leaving 2 subgoals.

Apply unknownprop_601e47e4d78cdf42e2a3e2d8b99d86f42d29aff46b5fc48aae50649fe35bd708 with x0, x2, x3, x4 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H3.

Apply unknownprop_e80a70fc28b36440a1efd4bd8be21f42fa8778462d8202d4a08b61486f7509ce with x1, x2, x3, x4 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H4.

■

Proofgold Proof