ChengsongTanPhdThesis/Chapters/Finite.tex
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  2073 	$a :: rs \grewrites \hflataux{a} @ rs$
  2073 	$a :: rs \grewrites \hflataux{a} @ rs$
  2074 \end{lemma}
  2074 \end{lemma}
  2075 \begin{proof}
  2075 \begin{proof}
  2076 	By induction on $a$. $rs$ is set to take arbitrary values.
  2076 	By induction on $a$. $rs$ is set to take arbitrary values.
  2077 \end{proof}
  2077 \end{proof}
  2078 It is also not surprising that $\textit{rsimp}$ will cover
  2078 It is also not surprising that 
  2079 the effect of $\hflataux{\_}$:
  2079 two regular expressions differing only in terms
       
  2080 of the
       
  2081 nesting of parentheses are equivalent w.r.t. $\textit{rsimp}$:
  2080 \begin{lemma}\label{cbsHfauRsimpeq1}
  2082 \begin{lemma}\label{cbsHfauRsimpeq1}
  2081 	$\rsimp{(r_1 + r_2)} = \rsimp{(\RALTS{\hflataux{r_1} @ \hflataux{r_2}})}$
  2083 	$\rsimp{(r_1 + r_2)} = \rsimp{(\RALTS{\hflataux{r_1} @ \hflataux{r_2}})}$
  2082 \end{lemma}
  2084 \end{lemma}
  2083 
  2085 
  2084 \begin{proof}
  2086 \begin{proof}