Let x0 of type ι be given.
Let x1 of type ι be given.
Apply ordsuccE with
x1,
x0,
x0 ⊆ x1 leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H2: x0 ∈ x1.
Apply H0 with
x0.
The subproof is completed by applying H2.
Assume H2: x0 = x1.
Apply H2 with
λ x2 x3 . x3 ⊆ x1.
The subproof is completed by applying Subq_ref with x1.