Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Assume H0: equip x0 x1.

Assume H1: equip x1 x2.

Apply H0 with equip x0 x2.

Let x3 of type ι → ι be given.

Assume H2: bij x0 x1 x3.

Apply H1 with equip x0 x2.

Let x4 of type ι → ι be given.

Assume H3: bij x1 x2 x4.

Let x5 of type ο be given.

Assume H4: ∀ x6 : ι → ι . bij x0 x2 x6 ⟶ x5.

Apply H4 with λ x6 . x4 (x3 x6).

Apply bij_comp with x0, x1, x2, x3, x4 leaving 2 subgoals.

The subproof is completed by applying H2.

The subproof is completed by applying H3.

■

Proofgold Proof