In the context of a general approach of studying properties of rewriting under strategies, we focus in this paper on the property of completeness of function definitions. We propose a procedure proving sufficient completeness of rewriting in the specific case of the innermost strategy, under the only assumption that the rewriting system innermost terminates on ground terms. It relies on an inductive proof that every ground term rewrites into a constructor term. The innermost rewriting relation on ground terms is simulated through an abstraction mechanism and narrowing. The inductive hypothesis allows assuming that terms smaller than the starting terms for an induction ordering rewrite into a constructor term. The existence of the induction ordering is checked during the proof process, by ensuring satisfiability of ordering constraints. An extension of this procedure is also proposed, to establish in the same time sufficient completeness and the needed innermost termination property.