Let x0 of type ι be given.
Let x1 of type ι be given.
Apply tuple_2_0_eq with
x0,
x1,
λ x2 x3 . SNo_pair x2 x1 ∈ complex.
Apply tuple_2_1_eq with
x0,
x1,
λ x2 x3 . SNo_pair (ap (lam 2 (λ x4 . If_i (x4 = 0) x0 x1)) 0) x2 ∈ complex.
Apply ReplI with
setprod real real,
λ x2 . SNo_pair (ap x2 0) (ap x2 1),
lam 2 (λ x2 . If_i (x2 = 0) x0 x1).
Apply tuple_2_setprod with
real,
real,
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.