proposition: Lemma Rsup_ub x0 E : has_sup E -> (ubound E) (supremum x0 E).
proof: Proof. by move=> supE x Ex; apply/ge_supremum_Nmem => //; exact: Rsupremums_neq0. 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