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 Th17:
  m2 + m3 c= m1 implies (m1 - m2) - m3 = m1 - (m2 + m3)
proof
  assume m2 + m3 c= m1;
  then (m1 - m2) - m3 = ((m1 - (m2 + m3)) + (m2 + m3)) - m2 - m3 by Th15
    .= (((m1 - (m2 + m3) + m3) + m2) - m2) - m3 by Th11
    .= ((m1 - (m2 + m3)) + m3) - m3 by Th16
    .= m1 - (m2 + m3) by Th16;
  hence thesis;
end;
