Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ο be given.
Apply famunionE_impred with
x0,
λ x6 . {mul_SNo (add_SNo 1 (mul_SNo (add_SNo x7 (minus_SNo x1)) x6)) (x3 x7)|x7 ∈ x2},
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x6 of type ι be given.
Assume H2: x6 ∈ x0.
Apply ReplE_impred with
x2,
λ x7 . mul_SNo (add_SNo 1 (mul_SNo (add_SNo x7 (minus_SNo x1)) x6)) (x3 x7),
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply H1 with
x6.
The subproof is completed by applying H2.