proposition: Lemma setCU_Efin (A : set T) (B : set \bar T) : ps_infty B -> ~` (EFin @` A) `&` ~` B = (EFin @` ~` A) `|` ([set -oo%E; +oo%E] `&` ~` B).
proof: Proof. move=> ps_inftyB. have -> : ~` (EFin @` A) = EFin @` (~` A) `|` [set -oo; +oo]%E. by rewrite EFin_setC setDKU // => x [|] -> -[]. rewrite setIUl; congr (_ `|` _); rewrite predeqE => -[x| |]; split; try by case. by move=> [] x' Ax' [] <-{x}; split; [exists x'|case: ps_inftyB => // -[]]. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop) reals ereal signed topology numfun normedtype HB(structures) sequences esum measure real_interval realfun exp lebesgue_stieltjes_measure