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

theorem
  not (x = -infty & y = -infty) & not (y = -infty & z = +infty) & x <= z
  + y implies y <> -infty
proof
  assume that
A1: not(x=-infty & y=-infty) and
A2: not(y = -infty & z = +infty) and
A3: x <= z + y;
    assume
A4: y = -infty;
    then z + y = -infty by A2,Def2;
    hence contradiction by A1,A3,A4,XXREAL_0:6;
end;
