Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ι be given.
Let x5 of type ι → ο be given.
Let x6 of type ι → ο be given.
Let x7 of type ι be given.
Assume H0: ∀ x8 . x8 ∈ x0 ⟶ x1 x8 = x2 x8.
Assume H1: ∀ x8 . x8 ∈ x0 ⟶ x3 x8 = x4 x8.
Assume H2:
∀ x8 . x8 ∈ x0 ⟶ iff (x5 x8) (x6 x8).
Apply L3 with
λ x8 x9 . lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) (lam x0 x1) (If_i (x10 = 2) (lam x0 x3) (If_i (x10 = 3) (Sep x0 x5) x7)))) = lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) x8 (If_i (x10 = 2) (lam x0 x4) (If_i (x10 = 3) (Sep x0 x6) x7)))).
Apply L4 with
λ x8 x9 . lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) (lam x0 x1) (If_i (x10 = 2) (lam x0 x3) (If_i (x10 = 3) (Sep x0 x5) x7)))) = lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) (lam x0 x1) (If_i (x10 = 2) x8 (If_i (x10 = 3) (Sep x0 x6) x7)))).
Apply L5 with
λ x8 x9 . lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) (lam x0 x1) (If_i (x10 = 2) (lam x0 x3) (If_i (x10 = 3) (Sep x0 x5) x7)))) = lam 5 (λ x10 . If_i (x10 = 0) x0 (If_i (x10 = 1) (lam x0 x1) (If_i (x10 = 2) (lam x0 x3) (If_i (x10 = 3) x8 x7)))).
Let x8 of type ι → ι → ο be given.