Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ο be given.
Assume H0:
∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . tuple_p (x1 x3) x4 ⟶ (∀ x5 . x5 ∈ x1 x3 ⟶ ap x4 x5 ∈ c8f46.. x0 (λ x6 . x1 x6)) ⟶ (∀ x5 . x5 ∈ x1 x3 ⟶ x2 (ap x4 x5)) ⟶ x2 (lam 2 (λ x5 . If_i (x5 = 0) x3 x4)).
Claim L1:
∀ x3 . 59caa.. x0 x1 x3 ⟶ x2 x3Apply unknownprop_9b1382fd828c310f237a34618b8aad95180eb391959d046ef1956fa7f3460a59 with
x0,
x1,
λ x3 . x2 x3.
Let x3 of type ι be given.
Assume H1: x3 ∈ x0.
Let x4 of type ι be given.
Assume H3:
∀ x5 . x5 ∈ x1 x3 ⟶ 59caa.. x0 x1 (ap x4 x5).
Assume H4:
∀ x5 . x5 ∈ x1 x3 ⟶ x2 (ap x4 x5).
Apply H0 with
x3,
x4 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x5 of type ι be given.
Assume H5: x5 ∈ x1 x3.
Apply unknownprop_a09e2d42c260dbb4e7d78819c18a31c6bb7fc9197f49b10e3eb42edd432f4e04 with
x0,
x1,
ap x4 x5.
Apply H3 with
x5.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
Let x3 of type ι be given.
Assume H2:
x3 ∈ c8f46.. x0 (λ x4 . x1 x4).
Apply L1 with
x3.
Apply unknownprop_9d3883c96dd9b5c53e4f6141d750f76e58929b6b233cf6b1779125f19b767e11 with
x0,
x1,
x3.
The subproof is completed by applying H2.