proposition: Lemma set_CC A B E: sub B E -> (E -s (A -s B)) = (E -s A) \cup B.
proof: Proof. move => be; set_extens t. case/setC_P => te td; apply/setU2_P. case: (setC_ni td)=> ta; [left | right]; fprops. move => h; apply /setC_P;case /setU2_P :h. by case /setC_P => te ta;split => //;case/setC_P. by move => tB;split; [ apply: be |case/setC_P ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)