proposition: Lemma Rsupremums_neq0 E : has_sup E -> (supremums E !=set0)%classic.
proof: Proof. by move=> /Rcondcomplete[x [? ?]]; exists x. 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