reserve i,j,k,l for Nat,
  x,x1,x2,y1,y2 for set;
reserve P,p,x,y,x1,x2 for set,
  m1,m2,m3,m4,m for marking of P,
  i,j,j1,j2,k,k1,k2,l,l1 for Nat;

theorem
  m1 c= m2 implies m2 - m1 c= m2
proof
  assume
A1: m1 c= m2;
  let p;
  assume p in P;
  then
A2: (m2 - m1).p = m2.p - m1.p by A1,Def5;
  m2.p - 0 = m2.p;
  hence thesis by A2,XREAL_1:13;
end;
