
theorem LemmaAuxIrr:
  for P,R being Relation st P misses R holds
    P~ misses R~
  proof
    let P,R be Relation;
    assume P misses R; then
    P /\ R = {} by XBOOLE_0:def 7; then
A1: (P /\ R)~ = {};
    (P /\ R)~ = P~ /\ R~ by RELAT_1:22;
    hence thesis by XBOOLE_0:def 7,A1;
  end;
