Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H1: x1 0.
Apply ordsuccE with
u9,
x0,
x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply cases_9 with
x0,
x1 leaving 10 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
Apply H11 with
λ x2 x3 . x1 x3.
The subproof is completed by applying H10.