Let x0 of type ι → (ι → (((ι → ο) → ο) → ο) → ο) → (((ι → ο) → ο) → ο) → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → (((ι → ο) → ο) → ο) → ο . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x1 . 77406.. x0 x1 (59fb5.. x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo4_prop with
77406.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : (((ι → ο) → ο) → ο) → ο . 77406.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (59fb5.. x0).
Apply unknownprop_18cd866ccb0a19c67a05e915ca593a5349638dce8b831707d9664a24cf991be3 with
x0,
x1,
59fb5.. x0.
The subproof is completed by applying H1.
Apply unknownprop_68a091797cc1b74fbeb69d1e3f550a7da314a5e4727ec9c3c922acad71190280 with
x0,
x1.
The subproof is completed by applying H0.