Let x0 of type ι be given.
Let x1 of type ο be given.
Assume H1:
∀ x2 . x2 ∈ real ⟶ ∀ x3 . x3 ∈ real ⟶ x0 = SNo_pair x2 x3 ⟶ x1.
Apply ReplE_impred with
setprod real real,
λ x2 . SNo_pair (ap x2 0) (ap x2 1),
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Apply H1 with
ap x2 0,
ap x2 1 leaving 2 subgoals.
Apply ap0_Sigma with
real,
λ x3 . real,
x2.
The subproof is completed by applying H2.
Apply ap1_Sigma with
real,
λ x3 . real,
x2.
The subproof is completed by applying H2.