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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNoLe 0 x0.
Apply sqrt_SNo_nonneg_prop1 with x0, mul_SNo (sqrt_SNo_nonneg x0) (sqrt_SNo_nonneg x0) = x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: and (SNo (sqrt_SNo_nonneg x0)) (SNoLe 0 (sqrt_SNo_nonneg x0)).
Assume H3: mul_SNo (sqrt_SNo_nonneg x0) (sqrt_SNo_nonneg x0) = x0.
The subproof is completed by applying H3.
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