Lemmas about intern-in-package-of-symbol available in the std/basic library.
Theorem:
(defthm equal-of-intern-in-package-of-symbols (implies (and (stringp a) (stringp b) (symbolp in-pkg)) (equal (equal (intern-in-package-of-symbol a in-pkg) (intern-in-package-of-symbol b in-pkg)) (equal a b))))