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 . x4 ∈ x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply unknownprop_30ddc768878844a84528ac4e845a2f81437458ecc81ad73fcb6b32ab7dec1955 with
x0,
x1,
In_rec_Vo4 x0 x1,
x0 x1 (In_rec_Vo4 x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_5f32da66d57eeaba7a1d19841e1b8f1005019fa8fa58df386168e4a64dad34fb with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_549ed4d6ab13405e2f934e782135a7d2cf08b083a9012f7772cc79fa3b0026c5 with
x0,
x1.
The subproof is completed by applying H0.