Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Assume H0: x2 ∈ x0.
Let x3 of type ι be given.
Assume H2:
∀ x4 . x4 ∈ x1 x2 ⟶ 59caa.. x0 x1 (ap x3 x4).
Let x4 of type ι → ο be given.
Assume H3:
∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . tuple_p (x1 x5) x6 ⟶ (∀ x7 . x7 ∈ x1 x5 ⟶ x4 (ap x6 x7)) ⟶ x4 (lam 2 (λ x7 . If_i (x7 = 0) x5 x6)).
Apply H3 with
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x5 of type ι be given.
Assume H4: x5 ∈ x1 x2.
Apply H2 with
x5,
x4 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H3.