proposition: Lemma interval_unbounded_setT (X : set R) : is_interval X -> ~ has_lbound X -> ~ has_ubound X -> X = setT.
proof: Proof. move=> iX lX uX; rewrite predeqE => x; split => // _. move/has_lbPn : lX => /(_ x) [y Xy xy]. move/has_ubPn : uX => /(_ x) [z Xz xz]. by apply: (iX y z); rewrite ?ltW. 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