Let x0 of type ι be given.
Assume H1: 1 ∈ x0.
Apply H2 with
x0,
0 leaving 2 subgoals.
The subproof is completed by applying SingI with x0.
Apply nat_trans with
x0,
1,
0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying In_0_1.
Apply In_no2cycle with
0,
1 leaving 2 subgoals.
The subproof is completed by applying In_0_1.
Apply SingE with
x0,
0,
λ x1 x2 . 1 ∈ x2 leaving 2 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H1.