Let x0 of type ι → (ι → ι → ο) → ι → ο be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ο . (∀ x4 . prim1 x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Apply In_ind with
λ x1 . 1d55d.. x0 x1 (In_rec_Vo1 x0 x1).
Let x1 of type ι be given.
Apply Descr_Vo1_prop with
1d55d.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2:
∀ x3 : ι → ο . 1d55d.. x0 x1 x3 ⟶ x2.
Apply H2 with
x0 x1 (In_rec_Vo1 x0).
Apply unknownprop_6b9d466c48459997b5943e2bfa8effee1803540eeebe30604246716ec482ccac with
x0,
x1,
In_rec_Vo1 x0.
The subproof is completed by applying H1.
Apply unknownprop_4a87b3b2bcf10bd0616cd3b0459f4ca1014c4bcd0183902ba6aaa9f0fef066b0 with
x0,
x1.
The subproof is completed by applying H0.