Let x0 of type ι → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Let x3 of type ι → ο be given.
Let x4 of type ι be given.
Let x5 of type ι → ο be given.
Assume H4: x0 x4 x5.
Apply PNoLtEq_tra with
x4,
x1,
x5,
x2,
x3 leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
Apply H2 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H1.