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EQness of functions

The case of
 (let ((f #'(lambda ...)))
      (eq f f))
has no bearing on the issue of whether (eq f #'eq) is valid.  #'eq means
(function eq), which may or may not result in something being done at
run time to evaluate it; f is a variable reference whose value has already
"been evaluated" at some prior time.  (eq f f) ought to always be true,
modulo some kinds of number-optimization.