Theorem :- Let M=(Q,S,δ,q0,F) be an Finite Automate and has n number of states. Let L be the regular language accepted by M .Let for every string x in L, there exists a constant n such that |x|>=n. Now , if the string x can be broken into three sub strings u,v and w such that
x=uvw
satisfying the following constraints :
1. v≠ ɛ i.e., |v|>=0
2. |uv|<= n
then uv1w is in L for i>=0
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lemma
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A lemma, or a subsidiary math theorem, is a theorem that one proves as an interim stage in proving another theorem. Lemmas can be viewed as scaffolding for the proof. Usually, they are not that interesting in and of themselves, but there are exceptions. See the related link for examples of lemmas that are famous independently of the main theorems.