Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → ο be given.
Apply orIR with
PNoLt x0 x1 x0 x2,
and (x0 = x0) (PNoEq_ x0 x1 x2).
Apply andI with
x0 = x0,
PNoEq_ x0 x1 x2 leaving 2 subgoals.
Let x3 of type ι → ι → ο be given.
Assume H1: x3 x0 x0.
The subproof is completed by applying H1.
The subproof is completed by applying H0.