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 Th15:
  m1 c= m2 implies m2 = (m2 - m1) + m1
proof
  assume
A1: m1 c= m2;
  let p be object;
  assume
A2: p in P;
  then ((m2 - m1) + m1).p = (m2 - m1).p + m1.p by Def4
    .= m2.p - m1.p + m1.p by A1,A2,Def5
    .= m2.p;
  hence thesis;
end;
