Assume H0: (λ x0 x1 . x1) = λ x0 x1 . x0.
Apply neq_0_1.
Apply H0 with
λ x0 x1 : ι → ι → ι . x1 1 0 = (λ x2 x3 . x2) 1 0.
Let x0 of type ι → ι → ο be given.
Assume H1: x0 ((λ x1 x2 . x1) 1 0) ((λ x1 x2 . x1) 1 0).
The subproof is completed by applying H1.