
theorem Th1:
  for x, y being Real st x >= 0 & max (x,y) = 0 holds x = 0
proof
  let x, y be Real;
  assume that
A1: x >= 0 and
A2: max (x,y) = 0;
  per cases by XXREAL_0:16;
  suppose
    max (x,y) = x;
    hence thesis by A2;
  end;
  suppose
A3: max (x,y) = y;
    then x <= y by XXREAL_0:25;
    hence thesis by A1,A2,A3,XXREAL_0:1;
  end;
end;
