Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
equip x1 x0.
Let x2 of type ι → ι be given.
Let x3 of type ο be given.
Assume H2:
∀ x4 : ι → ι . bij x1 x0 x4 ⟶ x3.
Apply H2 with
inv x0 x2.
Apply bij_inv with
x0,
x1,
x2.
The subproof is completed by applying H1.