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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, SNo (sqrt_SNo_nonneg 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.
Apply H2 with SNo (sqrt_SNo_nonneg x0).
Assume H4: SNo (sqrt_SNo_nonneg x0).
Assume H5: SNoLe 0 (sqrt_SNo_nonneg x0).
The subproof is completed by applying H4.