proposition: Lemma bound_itvE (R : numDomainType) (a b : R) : ((a \in `[a, b]) = (a <= b)) * ((b \in `[a, b]) = (a <= b)) * ((a \in `[a, b[) = (a < b)) * ((b \in `]a, b]) = (a < b)) * (a \in `[a, +oo[) * (a \in `]-oo, a]).
proof: Proof. by rewrite !(boundr_in_itv, boundl_in_itv). Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule