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I have came across following facts while reading some compilers related text. However I did not find them in any standard reference book (mainly dragon book). Are they correct? If yes, how can we prove them?

Fact:

  1. If there is a λ-free LL(1) grammar for a language, then we can also prepare SLR(1) grammar for it. (λ-free means: there is no null productions of the form $A\rightarrow\lambda$ for any non terminal $A$)
  2. LL(1) grammar whose variable are all able to derive a not null string is LALR(1). (able to derive a not null string means: there may exist null production $A\rightarrow \lambda$, but along with it, there should also exist non-null production $A\rightarrow \alpha$ for every such $A$, where $\alpha = (V+t)^*$ where $V$ is any non terminal and $t$ is any terminal)
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