Proofgold Proof

pf

Let x0 of type ι be given.

Let x1 of type ι be given.

Apply Empty_eq with SNo_sqrtauxset x0 0 x1.

Let x2 of type ι be given.

Assume H0: x2 ∈ SNo_sqrtauxset x0 0 x1.

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

The subproof is completed by applying H0.

Let x3 of type ι be given.

Assume H1: x3 ∈ x0.

Let x4 of type ι be given.

Assume H2: x4 ∈ 0.

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

Apply EmptyE with x4.

The subproof is completed by applying H2.

■