  This paper provides, over Henselian valued fields, some theorems on implicit
function and of Artin--Mazur on algebraic power series. Also discussed are
certain versions of the theorems of Abhyankar--Jung and Newton--Puiseux. The
latter is used in analysis of functions of one variable, definable in the
language of Denef--Pas, to obtain a theorem on existence of the limit, proven
over rank one valued fields in one of our recent papers. This result along with
the technique of fiber shrinking (developed there over rank one valued fields)
were, in turn, two basic tools in the proof of the closedness theorem.
