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 ⟶ ap x3 x4 ∈ c8f46.. x0 (λ x5 . x1 x5).
Apply unknownprop_a09e2d42c260dbb4e7d78819c18a31c6bb7fc9197f49b10e3eb42edd432f4e04 with
x0,
x1,
lam 2 (λ x4 . If_i (x4 = 0) x2 x3).
Apply unknownprop_ed3562c3cc27039b6bf218421c9238ae64a1c1c7e7329d5c626a1feffa8c1921 with
x0,
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Assume H3: x4 ∈ x1 x2.
Apply unknownprop_9d3883c96dd9b5c53e4f6141d750f76e58929b6b233cf6b1779125f19b767e11 with
x0,
x1,
ap x3 x4.
Apply H2 with
x4.
The subproof is completed by applying H3.