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Seems obvious but I need mathematical proof

I tried to go by knowing $R^*=\epsilon + RR^*$ but reached nothing

Parsa Noori
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    I don’t know what rules you have available for manipulating regular sets. Can you justify this calculation? $$(a+b)^=\epsilon(a+b)^\subseteq a^(a+b)^\subseteq(a+b)^(a+b)^=(a+b)^*$$ – Brian M. Scott Oct 03 '20 at 00:05
  • I'm new to regular expression and Kleene's algebra and ... but it seems like that your calculation is simply convincing for me – Parsa Noori Oct 03 '20 at 00:16
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    Basically it just uses the facts that $R^=R^R^$, and that if $R\subseteq S$, then $R^\subseteq S^*$, which shouldn’t be too hard to prove from any reasonable definition of the notation, so at worst it might require a little more justification for one or two of the steps. – Brian M. Scott Oct 03 '20 at 00:22
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    I think you're right – Parsa Noori Oct 03 '20 at 00:24

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