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denote a collection of ''n'' [[indeterminate (variable)|indeterminate]]s,
''k'''''<nowiki>[[x]]</nowiki>''' the [[ring (mathematics)|ring]] of formal power series with indeterminates '''x''' over a field ''k'', and
: '''y''' = ''y''<sub>1</sub>, …, ''y''<sub>''m''</sub>
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:''f''('''x''', '''y''') = 0
be a system of [[polynomial equation]]s in ''k''['''x''', '''y'''], and ''c'' a positive [[integer]]. Then given a formal power series solution '''ŷ'''('''x''') ∈ ''k'''''<nowiki>[[x]]</nowiki>''' there is an algebraic solution '''y'''('''x''') consisting of [[algebraic function]]s such that
:'''ŷ'''('''x''') ≡ '''y'''('''x''') mod ('''x''')<sup>''c''</sup>.
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