Let x0 of type ι → ο be given.

Let x1 of type ι → ο be given.

Let x2 of type ι be given.

Assume H0: x1 x2.

Apply orIR with ∃ x3 . and (x0 x3) (6c5f4.. x2 = 0b8ef.. x3), ∃ x3 . and (x1 x3) (6c5f4.. x2 = 6c5f4.. x3).

Let x3 of type ο be given.

Assume H1: ∀ x4 . and (x1 x4) (6c5f4.. x2 = 6c5f4.. x4) ⟶ x3.

Apply H1 with x2.

Apply andI with x1 x2, 6c5f4.. x2 = 6c5f4.. x2 leaving 2 subgoals.

The subproof is completed by applying H0.

Let x4 of type ι → ι → ο be given.

Assume H2: x4 (6c5f4.. x2) (6c5f4.. x2).

The subproof is completed by applying H2.

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Proofgold Proof