Sergey Karavashkin: 
 >
 >No smokescreen. I have presented just the proof.

  Then write down the scalar function \Phi for which you assert
the relation, \nabla x (\nabla\Phi) = 0 does not hold. Don't
give me a bunch of interpretational mumbo-jumbo, just write
the scalar function.

 >Determine the circulation of vector in my diagram and after this state
 >curl(grad(phi)) = 0 identically.

  Write down the function \phi. I'm not going to sort through whatever
contortions you've gone through to get the wrong answer the hard way.
Just give me the function.
 
 >Still I see the smokescreen from your
 >side, but the wing is from mine - this is why you are suffocating with
 >your own smokescreen. Until you understand it, this will irritate your
 >eyes. Your, not mine. ;-)
 
  Write down the scalar function. Don't add any of your personal
interpretations or try to ``explain'' how I have to calculate
something to get your answer. Just give me a scalar function.
I can take a gradient and curl.