Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → ο be given.
Assume H0:
PNoLt x0 x1 x0 x2.
Apply unknownprop_7d798c5794ed96c61cc9ec828963a5831eee43021e8f1ea48be05a5cb53904e0 with
x0,
x0,
x1,
x2,
PNoLt_ x0 x1 x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying unknownprop_58a6c05ee842205b1830f4215e2d37c45feb2bdaf9c3b043b073760369d7073f with
x0,
λ x3 x4 . PNoLt_ x3 x1 x2.
Apply FalseE with
PNoEq_ x0 x1 x2 ⟶ x2 x0 ⟶ PNoLt_ x0 x1 x2.
Apply unknownprop_60a0545f75dffa8edcef0ebd95f0c8e1071ecdfa5679c45641fd22ee51a570c9 with
x0.
The subproof is completed by applying H1.
Apply FalseE with
PNoEq_ x0 x1 x2 ⟶ not (x1 x0) ⟶ PNoLt_ x0 x1 x2.
Apply unknownprop_60a0545f75dffa8edcef0ebd95f0c8e1071ecdfa5679c45641fd22ee51a570c9 with
x0.
The subproof is completed by applying H1.