Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → ο be given.
Apply unknownprop_1c12738cd89f8c615a541c15b6797bba2a5be97ab5e514c9fd76b3fef06e2aa9 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_0db3801abb119083deb2ee4735186fa96fbe6d2310a78ac3cc07b41d547f4c2e with
x0,
λ x3 x4 . PNoLt_ x3 x1 x2.
Apply FalseE with
PNoEq_ x0 x1 x2 ⟶ x2 x0 ⟶ PNoLt_ x0 x1 x2.
Apply In_irref with
x0.
The subproof is completed by applying H1.
Apply FalseE with
PNoEq_ x0 x1 x2 ⟶ not (x1 x0) ⟶ PNoLt_ x0 x1 x2.
Apply In_irref with
x0.
The subproof is completed by applying H1.