reserve a,b,c for set;

theorem
  for D being non empty set,CR,r being File of D holds addcr(r,CR)=
  ovlldiff(r,CR)^CR
proof
  let D be non empty set,CR,r be File of D;
  thus addcr(r,CR) = ovlcon(r,CR) by FINSEQ_8:def 11
    .= ovlldiff(r,CR)^(ovlpart(r,CR)^ovlrdiff(r,CR)) by FINSEQ_8:12
    .= ovlldiff(r,CR)^CR by Th31;
end;
