Let x0 of type (CT2 (ι → ι → ι)) → ι → ι → ι be given.

Assume H0: ∀ x1 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 64789.. x1 ⟶ fb516.. (x0 x1).

Apply unknownprop_ab4214f1a2c3a2db87f0adca5ced74f7623bce7b4515d8ff0b65e6c4b80e6cfc with λ x1 : ι → ι → ι . f9ee2.. (λ x2 : ι → ι → ι . x0 (λ x3 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x3 x1 x2)).

Let x1 of type ι → ι → ι be given.

Assume H1: fb516.. x1.

Apply unknownprop_ab4214f1a2c3a2db87f0adca5ced74f7623bce7b4515d8ff0b65e6c4b80e6cfc with λ x2 : ι → ι → ι . x0 (λ x3 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x3 x1 x2).

Let x2 of type ι → ι → ι be given.

Assume H2: fb516.. x2.

Apply H0 with λ x3 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x3 x1 x2.

Apply and3I with (λ x3 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x3 x1 x2) = λ x3 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x3 x1 x2, fb516.. x1, fb516.. x2 leaving 3 subgoals.

Let x3 of type (CT2 (ι → ι → ι)) → (CT2 (ι → ι → ι)) → ο be given.

Assume H3: x3 (λ x4 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x4 x1 x2) (λ x4 : (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x4 x1 x2).

The subproof is completed by applying H3.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

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Proofgold Proof