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Proofgold Proof

pf
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 ιι be given.
Let x4 of type ι be given.
Assume H0: x4SNo_recipauxset x0 x1 x2 x3.
Let x5 of type ο be given.
Assume H1: ∀ x6 . x6x0∀ x7 . x7x2x4 = mul_SNo (add_SNo 1 (mul_SNo (add_SNo x7 (minus_SNo x1)) x6)) (x3 x7)x5.
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: x6x0.
Assume H3: x4{mul_SNo (add_SNo 1 (mul_SNo (add_SNo x7 (minus_SNo x1)) x6)) (x3 x7)|x7 ∈ x2}.
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.