Let x0 of type ι → (ι → ο) → ο be given.
Let x1 of type ι → (ι → ο) → ο be given.
Let x2 of type ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι be given.
Assume H1: x4 ∈ x2.
Apply H2 with
PNo_rel_strict_imv x0 x1 x4 x3.
Apply andI with
PNo_rel_strict_upperbd x0 x4 x3,
PNo_rel_strict_lowerbd x1 x4 x3 leaving 2 subgoals.
Apply PNo_rel_strict_upperbd_antimon with
x0,
x2,
x3,
x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply PNo_rel_strict_lowerbd_antimon with
x1,
x2,
x3,
x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.