Let x0 of type ι → (ι → ι → ι → ι) → ι → ι → ι be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ι → ι . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x1 . ca584.. x0 x1 (28408.. x0 x1).
Let x1 of type ι be given.
Apply Descr_iii_prop with
ca584.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ι → ι → ι . ca584.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (28408.. x0).
Apply unknownprop_142767f75c94b264786489e2c0fd020ad5ccbbef5fa29c33a75a8a6af352f10a with
x0,
x1,
28408.. x0.
The subproof is completed by applying H1.
Apply unknownprop_a88159a7ab366b8736dd3edc174eb90d0f6c3dce33f5f2e38d1ba66209147e31 with
x0,
x1.
The subproof is completed by applying H0.