proposition: Lemma RsqrtE x : 0 <= x -> sqrt x = Num.sqrt x.
proof: Proof. move => x0; apply/eqP; have [t1 t2] := conj (sqrtr_ge0 x) (sqrt_pos x). rewrite eq_sym -(eqrXn2 (_: 0 < 2)%N t1) //; last by apply /RleP. rewrite sqr_sqrtr // !exprS expr0 mulr1 -RmultE ?sqrt_sqrt //; by apply/RleP. Qed.
imports: Rdefinitions Raxioms RIneq Rbasic_fun Zwf Epsilon FunctionalExtensionality Ranalysis1 Rsqrt_def Rtrigo1 Reals mathcomp(all_ssreflect ssralg poly mxpoly ssrnum) HB(structures) mathcomp(boolp classical_sets) reals