Let x0 of type ι be given.
Let x1 of type 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 ⟶ x2 x4 x5 = x3 x4 x5.
Apply ReplEq_ext with
setprod x0 x1,
λ x4 . x2 (ap x4 0) (ap x4 1),
λ x4 . x3 (ap x4 0) (ap x4 1).
Let x4 of type ι be given.
Apply H0 with
ap x4 0,
ap x4 1 leaving 2 subgoals.
Apply ap0_Sigma with
x0,
λ x5 . x1,
x4.
The subproof is completed by applying H1.
Apply ap1_Sigma with
x0,
λ x5 . x1,
x4.
The subproof is completed by applying H1.