Proofgold Proof

pf

Let x0 of type ι be given.

Let x1 of type ι be given.

Apply Empty_eq with SNo_sqrtauxset 0 x0 x1.

Let x2 of type ι be given.

Assume H0: x2 ∈ SNo_sqrtauxset 0 x0 x1.

Apply SNo_sqrtauxset_E with 0, x0, x1, x2, False leaving 2 subgoals.

The subproof is completed by applying H0.

Let x3 of type ι be given.

Assume H1: x3 ∈ 0.

Apply FalseE with ∀ x4 . x4 ∈ x0 ⟶ SNoLt 0 (add_SNo x3 x4) ⟶ x2 = div_SNo (add_SNo x1 (mul_SNo x3 x4)) (add_SNo x3 x4) ⟶ False.

Apply EmptyE with x3.

The subproof is completed by applying H1.

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