prove that a function is an equivalence relation
Major Section:  EVENTS

(defequiv set-equal)

is an abbreviation for (defthm set-equal-is-an-equivalence (and (booleanp (set-equal x y)) (set-equal x x) (implies (set-equal x y) (set-equal y x)) (implies (and (set-equal x y) (set-equal y z)) (set-equal x z))) :rule-classes (:equivalence))

See equivalence.

General Form:
(defequiv fn
  :rule-classes rule-classes
  :instructions instructions
  :hints hints
  :otf-flg otf-flg
  :event-name event-name
  :doc doc)
where fn is a function symbol of arity 2, event-name, if supplied, is a symbol, and all other arguments are as specified in the documentation for defthm. The defequiv macro expands into a call of defthm. The name of the defthm is fn-is-an-equivalence, unless event-name is supplied, in which case event-name is the name used. The term generated for the defthm event states that fn is Boolean, reflexive, symmetric, and transitive. The rule-class :equivalence is added to the rule-classes specified, if it is not already there. All other arguments to the generated defthm form are as specified by the other keyword arguments above.