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$\begingroup$ Inspecting the proof of that library lemma eq_bool at github.com/coq/coq/blob/master/theories/Strings/Ascii.v#L74 , one can see that it’s proven there using an ad hoc local tactic t_eqb, designed for several “easy” equality lemmas like this that are given there, which simply automatically repeatedly tries applying basic lemmas on equality of Booleans and destructing the goal. $\endgroup$
– Peter LeFanu Lumsdaine
Commented Jun 28 at 9:58
$\begingroup$ @PeterLeFanuLumsdaine Generally speaking, if I have to dig into a library's implementation details in order to use it, then the library is not good enough... Encapsulation is a name for this. $\endgroup$
– Julio Di Egidio
Commented yesterday

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