Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H0:
PNoLt x0 x1 x0 x1.
Apply PNoLtE with
x0,
x0,
x1,
x1,
False leaving 4 subgoals.
The subproof is completed by applying H0.
Apply PNoLt_irref_ with
binintersect x0 x0,
x1.
The subproof is completed by applying H1.
Assume H1: x0 ∈ x0.
Apply FalseE with
PNoEq_ x0 x1 x1 ⟶ x1 x0 ⟶ False.
Apply In_irref with
x0.
The subproof is completed by applying H1.
Assume H1: x0 ∈ x0.
Apply FalseE with
PNoEq_ x0 x1 x1 ⟶ not (x1 x0) ⟶ False.
Apply In_irref with
x0.
The subproof is completed by applying H1.