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

theorem
  t <> -infty & t <> +infty & x < y implies x + t < y + t
proof
  assume that
A1: t <> -infty & t <> +infty and
A2: x < y;
A3: t-t = 0 by Th7;
A4: now
    assume x + t = y + t;
    then x + (t -t) = y + t-t by A1,Th30;
    then x+ 0 = y + (t-t) by A1,A3,Th30;
    then x=y+ 0 by A3,Th4;
    hence contradiction by A2,Th4;
  end;
  x + t <= y + t by A2,Th36;
  hence thesis by A4,XXREAL_0:1;
end;
