Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: x2 ∈ x1.
Apply ordsuccE with
x0,
x1,
x2 ∈ ordsucc x0 leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H3: x1 ∈ x0.
Apply ordsuccI1 with
x0,
x2.
Apply H0 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
Assume H3: x1 = x0.
Apply ordsuccI1 with
x0,
x2.
Apply H3 with
λ x3 x4 . x2 ∈ x3.
The subproof is completed by applying H2.