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

theorem
  0 <= a & 0 <= b & a <>b implies 1/(sqrt a+sqrt b) = (sqrt a - sqrt b)/ (a-b)
proof
  assume that
A1: 0 <= a and
A2: 0 <= b and
A3: a <>b;
  thus 1/(sqrt a+sqrt b) = (sqrt a - sqrt b)/((sqrt a)^2-(sqrt b)^2) by A1,A2
,A3,Lm5,Th10
    .= (sqrt a - sqrt b)/(a-(sqrt b)^2) by A1,Def2
    .= (sqrt a - sqrt b)/(a-b) by A2,Def2;
end;
