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

theorem Th30:
  not (x = +infty & y = -infty) & not (x = -infty & y = +infty) &
not (y = +infty & z = +infty) & not (y = -infty & z = -infty) & not (x = +infty
  & z = +infty) & not (x = -infty & z = -infty) implies x + y - z = x + (y - z)
proof
  assume that
A1: ( not (x = +infty & y = -infty))& not (x = -infty & y = +infty) and
A2: ( not (y = +infty & z = +infty))& not (y = -infty & z = -infty) and
A3: ( not (x = +infty & z = +infty))& not (x = -infty & z = -infty);
A4: ( not (x = +infty & -z = -infty))& not (x = -infty & -z = +infty) by A3
,Th23;
  ( not (y = +infty & -z = -infty))& not (y = -infty & -z = +infty) by A2,Th23;
  hence thesis by A1,A4,Th29;
end;
