reserve x,y,z for Element of REAL+;

theorem
  z <=' x & y <=' z implies x -' z + y = x -' (z -' y)
proof
  assume that
A1: z <=' x and
A2: y <=' z;
  thus x -' (z -' y) = x + y -' z by A2,Lm11
    .= x -' z + y by A1,Th13;
end;
