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= m1 implies m1 = m2
proof
  assume
A1: m1 c= m2;
  assume
A2: m2 c= m1;
  let p be object;
  assume
A3: p in P;
  then
A4: m1.p <= m2.p by A1;
  m2.p <= m1.p by A2,A3;
  hence thesis by A4,XXREAL_0:1;
end;
