Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2:
x2 ∈ ap x0 x1.
Apply H0 with
λ x3 x4 . lam 2 (λ x5 . If_i (x5 = 0) x1 x2) ∈ x4.
Apply tuple_2_Sigma with
omega,
λ x3 . ap x0 x3,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.