reserve a,b,c,x,y,z for Real;

theorem
  0 <= a & 0 <= b implies (sqrt a - sqrt b)*(sqrt a + sqrt b) = a - b
proof
  assume that
A1: 0 <= a and
A2: 0 <= b;
  thus (sqrt a - sqrt b)*(sqrt a + sqrt b) = (sqrt a)^2 - (sqrt b)^2
    .= a - (sqrt b)^2 by A1,Def2
    .= a - b by A2,Def2;
end;
