Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0:
x1 ∈ prim4 x0.
Apply PowerI with
ordsucc x0,
binunion x1 (Sing x0).
Let x2 of type ι be given.
Apply binunionE with
x1,
Sing x0,
x2,
x2 ∈ ordsucc x0 leaving 3 subgoals.
The subproof is completed by applying H1.
Assume H2: x2 ∈ x1.
Apply ordsuccI1 with
x0,
x2.
Apply PowerE with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply SingE with
x0,
x2,
λ x3 x4 . x4 ∈ ordsucc x0 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying ordsuccI2 with x0.