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given a $\lambda \text{-}$term $M$, how does one prove that the identity substitution on $M$ results in $M$ ? That is:$$[x/x] M \equiv M$$

Should I go for the cases, trying to prove for $M$ atomic, for $M = \lambda x.N$ and for $M = AB\;$?

If not, what approach should I use to prove that?

Daniel
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    Why not try proving it by cases and find out if it works? If you run into trouble, ask a question then stating what you tried and where you got stuck. – Derek Elkins left SE Aug 23 '17 at 19:12

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