Let x0 of type ι 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.
Apply unknownprop_9c4323d14785b84a66d449068a5854b52f7f14bc003d3f63275870fa29b9e25d with
λ x4 x5 : ι → (ι → ο) → ι → (ι → ο) → ο . x5 x0 x2 x1 x3 ⟶ ∀ x6 : ο . (PNoLt x0 x2 x1 x3 ⟶ x6) ⟶ (x0 = x1 ⟶ PNoEq_ x0 x2 x3 ⟶ x6) ⟶ x6.
Assume H0:
(λ x4 . λ x5 : ι → ο . λ x6 . λ x7 : ι → ο . or (PNoLt x4 x5 x6 x7) (and (x4 = x6) (PNoEq_ x4 x5 x7))) x0 x2 x1 x3.
Let x4 of type ο be given.
Assume H1:
PNoLt x0 x2 x1 x3 ⟶ x4.
Assume H2:
x0 = x1 ⟶ PNoEq_ x0 x2 x3 ⟶ x4.
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with
PNoLt x0 x2 x1 x3,
and (x0 = x1) (PNoEq_ x0 x2 x3),
x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply andE with
x0 = x1,
PNoEq_ x0 x2 x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.