Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H0:
∀ x2 . x1 x2 ⟶ ∀ x3 . x3 ∈ x2 ⟶ nIn x0 x3.
Assume H1: x1 0.
Let x2 of type ι be given.
Assume H2: x1 x2.
Apply pair_tag_0 with
x0,
x1,
x2,
λ x3 x4 . CD_proj1 x0 x1 x3 = 0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply CD_proj1_2 with
x0,
x1,
x2,
0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.