reserve r,s,t,u for Real;

theorem Th20:
  for X being RealLinearSpace, M1,M2 being Subset of X st M1 c= M2
  holds conv(M1) c= conv(M2)
proof
  let X be RealLinearSpace, M1,M2 be Subset of X;
  assume M1 c= M2;
  then Convex-Family M2 c= Convex-Family M1 by Th19;
  then
A1: meet (Convex-Family M1) c= meet (Convex-Family M2) by SETFAM_1:6;
  let x be object;
  assume x in conv(M1);
  hence thesis by A1;
end;
