Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0:
lam 2 (λ x5 . If_i (x5 = 0) x3 x4) ∈ Sep2 x0 x1 x2.
Claim L1:
and (and (x3 ∈ x0) (x4 ∈ x1 x3)) (x2 x3 x4)Apply Sep2E' with
x0,
x1,
x2,
x3,
x4.
The subproof is completed by applying H0.
Apply L1 with
x3 ∈ x0.
Assume H2:
and (x3 ∈ x0) (x4 ∈ x1 x3).
Assume H3: x2 x3 x4.
Apply H2 with
x3 ∈ x0.
Assume H4: x3 ∈ x0.
Assume H5: x4 ∈ x1 x3.
The subproof is completed by applying H4.