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.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Assume H1: x1 0.
Assume H2: x1 1.
Assume H3: x2 0 = 0.
Assume H4: x3 0 = 0.
Assume H5: x3 1 = 1.
Assume H6: ∀ x6 . x1 x6 ⟶ x4 0 x6 = x6.
Assume H7: ∀ x6 . x1 x6 ⟶ x4 x6 0 = x6.
Assume H8: ∀ x6 . x1 x6 ⟶ x5 0 x6 = 0.
Assume H9: ∀ x6 . x1 x6 ⟶ x5 x6 1 = x6.
Let x6 of type ι be given.
Apply CD_proj0_F with
x0,
x1,
1,
λ x7 x8 . pair_tag x0 (x4 (x5 (CD_proj0 x0 x1 x6) x8) (x2 (x5 (x3 (CD_proj1 x0 x1 1)) (CD_proj1 x0 x1 x6)))) (x4 (x5 (CD_proj1 x0 x1 1) (CD_proj0 x0 x1 x6)) (x5 (CD_proj1 x0 x1 x6) (x3 x8))) = x6 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply CD_proj1_F with
x0,
x1,
1,
λ x7 x8 . pair_tag x0 (x4 (x5 (CD_proj0 x0 x1 x6) 1) (x2 (x5 (x3 x8) (CD_proj1 x0 x1 x6)))) (x4 (x5 x8 (CD_proj0 x0 x1 x6)) (x5 (CD_proj1 x0 x1 x6) (x3 1))) = x6 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.