Let x0 of type ι → (ι → ι → ι → ο) → ι → ι → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ι → ο . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x1 . 6f52e.. x0 x1 (03431.. x0 x1).
Let x1 of type ι be given.
Apply Descr_iio_prop with
6f52e.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ι → ι → ο . 6f52e.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (03431.. x0).
Apply unknownprop_539172fd02c529de09e886b5940879e698f092d56b785ada1417814e30eb8f03 with
x0,
x1,
03431.. x0.
The subproof is completed by applying H1.
Apply unknownprop_f1193b6d6ed98f53e20a7c2c98b95043e1d349df91d36c172d7f2aee2f50f66e with
x0,
x1.
The subproof is completed by applying H0.