reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;

theorem
  y is real implies (z - y) + (y - x) = z - x
proof
  assume
A1: y is real;
  thus (z - y) + (y - x) = (z - y) - (x - y) by Th27
    .= z - x by A1,Th33;
end;
