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--- lfa:2024:lab11 [2026/01/18 17:53]
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+++ lfa:2024:lab11 [2026/01/18 17:55] (current)
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@@ Line 149: / Line 149: @@
 . **Basis**:
-In zero steps, we have $ \( A \Rightarrow{0}_G A \iff A \Rightarrow{0}_H A \) $.
+In zero steps, we have \( A \to^{0}_G A \iff A \to^{0}_H A \).
 . **Induction**:
-Assuming $ \( A \Rightarrow{*}_G w_1 B w_2 \iff A \Rightarrow{*}_H w_2^R B w_1^R \) $,
+Assuming \( A \to^{*}_G w_1 B w_2 \iff A \to^{*}_H w_2^R B w_1^R \),
-we can apply any production $ \( B \to u \) $ in \( G \) (and in \( H \) in reverse) and obtain:
+we can apply any production \( B \to u \) in \( G \) (and in \( H \) in reverse) and obtain:
-$ \( A \rightarrow^{*}_G w_1 u w_2 \) $
+\( A \to^{*}_G w_1 u w_2 \)
+\( A \to^{*}_H w_2^R u^R w_1^R \),   where indeed \( w_2^R u^R w_1^R \) is the reverse of \( w_1 u w_2 \).
-$ \( A \rightarrow^{*}_H w_2^R u^R w_1^R \) $,   where indeed $ \( w_2^R u^R w_1^R \) $ is the reverse of $ \( w_1 u w_2 \) $.
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