Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Assume H0: ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x1 x4 ⟶ x2 x4 x5 = x3 x4 x5.
Apply encode_u_ext with
x0,
λ x4 . lam (x1 x4) (λ x5 . x2 x4 x5),
λ x4 . lam (x1 x4) (λ x5 . x3 x4 x5).
Let x4 of type ι be given.
Assume H1: x4 ∈ x0.
Apply encode_u_ext with
x1 x4,
λ x5 . x2 x4 x5,
λ x5 . x3 x4 x5.
Let x5 of type ι be given.
Assume H2: x5 ∈ x1 x4.
Apply H0 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.