In the case of m+n variables we have n equations which must be satisfied for for the theorem to be applicable, althought (I understand that) there might be more than one solutions. But if for a given there are more than one satisfying the n equations (and I do not find any statement in the theorem preventing this) how can the theorem ensure that there is one and only one set of solutions which are continuous, satisfy and for which ? I mean how can f be a function?...Of course I must be missing something...

thanks a lot