proposition: Lemma set_itv_setT (i : interval R) : [set` i] = setT -> i = `]-oo, +oo[.
proof: Proof. have [i0 /(congr1 (@Rhull _))|] := boolP (neitv i). by rewrite set_itvK// => ->; exact: RhullT. by rewrite negbK => /eqP ->; rewrite predeqE => /(_ 0)[_]/(_ Logic.I). Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets functions) HB(structures) reals ereal signed topology normedtype sequences