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 & m2 c= m3 implies m3 - m2 c= m3 - m1
proof
  assume that
A1: m1 c= m2 and
A2: m2 c= m3;
A3: m1 c= m3 by A1,A2,Th2;
  let p;
  assume
A4: p in P;
  then
A5: m1.p <= m2.p by A1;
A6: (m3-m1).p = m3.p - m1.p by A3,A4,Def5;
  (m3-m2).p = m3.p - m2.p by A2,A4,Def5;
  hence thesis by A5,A6,XREAL_1:10;
end;
