Let x0 of type ι be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι be given.
Assume H0:
∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ x5 ∈ x0) ⟶ iff (x1 x4) (x2 x4).
Apply encode_c_ext with
x0,
x1,
x2.
The subproof is completed by applying H0.
Apply L1 with
λ x4 x5 . lam 3 (λ x6 . If_i (x6 = 0) x0 (If_i (x6 = 1) (encode_c x0 x1) x3)) = lam 3 (λ x6 . If_i (x6 = 0) x0 (If_i (x6 = 1) x4 x3)).
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H2.