The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping

The level set $M$ of a smooth mapping $F$ in a neighborhood of an anormal point is investigated. Concepts of 2-regularity are introduced for it. It is proved that if the mapping is 2-regular at the point under consideration, then in a neighborhood of it the set $M$ is locally diffeomorphic to the set of zeros of the second differential of $F$.