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
  m - {$}P = m
proof
A1: now
    let p;
    assume p in P;
    then ({$}P).p = 0 by Lm1;
    hence m.p = m.p - ({$}P).p;
  end;
  {$}P c= m by Th1;
  hence thesis by A1,Def5;
end;
