Let x0 of type ι → (ι → ι → ι) → ι → ι be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ι . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x1 . 61278.. x0 x1 (6445c.. x0 x1).
Let x1 of type ι be given.
Apply Descr_ii_prop with
61278.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ι → ι . 61278.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (6445c.. x0).
Apply unknownprop_2f69c8b239b7ebca0dc9cbfad7d9ad045222aa6f8486aafcef9fbefa96660c9c with
x0,
x1,
6445c.. x0.
The subproof is completed by applying H1.
Apply unknownprop_9d8fc65a67d6e314245c05f0fc90054d64caf3cbb263534564051fb62d74e653 with
x0,
x1.
The subproof is completed by applying H0.