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

theorem
  z <=' y implies x + (y -' z) = x + y - z
proof
  assume
A1: z <=' y;
  y <=' x + y by ARYTM_2:19;
  then z <=' x + y by A1,Th3;
  then x + y - z = x + y -' z by Def2;
  hence thesis by A1,Th13;
end;
