Hi, the negative introduction is assimilated to the positive and both mean "negative value".
---mica vero/ and ---non è mica vero/ mean the same; the first one is just an abbreviated form.
Explanation:
"Mica" is an archaic word for "mollica", the internal part of bread -- it remains on the table at the end of the lunch and it is thrown away: Thus it begun to be used as "with no value".
Curiously, a different idiom uses its synonym "briciole" (the single small pieces) when a person obtains just the smallest part of a value, and feels humiliated: You gave me only "briciole".
However, due to its origins, the using of Mica sounds colloquial but it may come out in intense speech (like any swear word).
It is also very similar to the use of Punto , which is used also in french (Point) to say "value almost 0":
-- (non) ce n'è punto = there is any
-- (non) ce n'è mica = there is any
So in this case you should not stick on Boolean algebra, as also in "non conosco nessuno" (I don't know "nobody") the use of a double negation is "wrong" but customary.
Hence Mica and Punto always mean "null" and -- due to their main colloquial context, which is meant to be "direct" -- they would never be used inside a complicated logic as double negation. ciao
!) apparent exception: ---mica male! (often said of a nice smt/sb): not bad at all = "very nice" -- Here is still not really a matter of logic but more of a speech figure "negating the opposite"