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: 8033b.. x0 x1 x2 x3.

Apply H2 with 8033b.. x0 x1 x2 x4.

Assume H3: 6f2c4.. x0 x2 x3.

Assume H4: dafc2.. x1 x2 x3.

Apply andI with 6f2c4.. x0 x2 x4, dafc2.. x1 x2 x4 leaving 2 subgoals.

Apply unknownprop_f8830730c453029980ff6e25a559072ec72cba902a9041568e89a9be9c674e28 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_c807b0bff53e9b983cb2d9b12ab43c2d93a7edbcf261d444edae95de9e135e35 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.

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Proofgold Proof