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

theorem
  0 <= b & b < a implies 1/(sqrt a-sqrt b) = (sqrt a + sqrt b)/(a-b)
proof
  assume that
A1: 0 <= b and
A2: b < a;
  thus 1/(sqrt a-sqrt b) = (sqrt a + sqrt b)/((sqrt a)^2-(sqrt b)^2) by A1,A2
,Lm5,Th11
    .= (sqrt a + sqrt b)/(a-(sqrt b)^2) by A1,A2,Def2
    .= (sqrt a + sqrt b)/(a-b) by A1,Def2;
end;
