Let x0 of type ι → (ι → ((ι → ο) → ο) → ο) → ((ι → ο) → ο) → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ((ι → ο) → ο) → ο . (∀ x4 . prim1 x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply unknownprop_e3fd7e34e0da9eea44164f3141ff6fc232704ab917a0a07eb8451b62e6e7b7c2 with
x0,
x1,
In_rec_Vo3 x0 x1,
x0 x1 (In_rec_Vo3 x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_fd514410ca8da3fccfdb89525bf3bbb90dae0114fbbe4b92682d3ee2a566d218 with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_2983c239ee68f51430d1cd05a4be8270ac120251debbce08fe470ec64aa3d910 with
x0,
x1.
The subproof is completed by applying H0.