theorem Th30:
  f tolerates g iff f \/ g = f +* g
proof
  thus f tolerates g implies f \/ g = f +* g
  proof
    assume f tolerates g;
    then
A1: f c= f +* g by Th28;
A2: f +* g c= f \/ g by Th29;
    g c= f +* g by Th25;
    then f \/ g c= f +* g by A1,XBOOLE_1:8;
    hence thesis by A2;
  end;
  thus thesis by PARTFUN1:51;
end;
