Let x0 of type ι be given.
Apply unknownprop_694898c9791aec4140fc01c2b4287388fd1297142d7e1ee2585d4a7ba4f43dce with
λ x1 x2 : ι → ο . x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ Subq (ordsucc x3) x0.
Assume H0:
∀ x1 . In x1 x0 ⟶ Subq x1 x0.
Let x1 of type ι be given.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with
ordsucc x1,
x0.
Let x2 of type ι be given.
Apply unknownprop_84fe37a922385756a4e0826a593defb788cadbe4bdc9a7fe6b519ea49f509df5 with
x1,
x2,
In x2 x0 leaving 3 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_cc8f63ddfbec05087d89028647ba2c7b89da93a15671b61ba228d6841bbab5e9 with
x1,
x0,
x2 leaving 2 subgoals.
Apply H0 with
x1.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Assume H3: x2 = x1.
Apply H3 with
λ x3 x4 . In x4 x0.
The subproof is completed by applying H1.