Apply neq_0_1.
set y0 to be 0
set y1 to be 1
Claim L1: ∀ x2 : ι → ο . x2 y1 ⟶ x2 y0
Let x2 of type ι → ο be given.
Assume H1: x2 1.
set y3 to be λ x3 . x2
Apply H0 with
λ x4 x5 : ι → ι → ι . x4 1 0 = 1,
λ x4 . y3 leaving 2 subgoals.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying L2.
Let x2 of type ι → ι → ο be given.
Apply L1 with
λ x3 . x2 x3 y1 ⟶ x2 y1 x3.
Assume H2: x2 y1 y1.
The subproof is completed by applying H2.