theorem Th135:
  r++F c= r++G implies F c= G
proof
  assume
A1: r++F c= r++G;
  let i;
  assume i in F;
  then r+i in r++F by Th132;
  then ex w st r+i = r+w & w in G by A1,Th134;
  hence thesis by XXREAL_3:11;
end;
