DEFCONG
prove congruence rule
Major Section: EVENTS
Defcong is used to prove that one equivalence relation preserves
another in a given argument position of a given function.
Example:
(defcong set-equal iff (memb x y) 2)
is an abbreviation for
(defthm set-equal-implies-iff-memb-2
(implies (set-equal y y-equiv)
(iff (memb x y) (memb x y-equiv)))
:rule-classes (:congruence))
See congruence and also see equivalence.
General Form:
(defcong equiv1 equiv2 term k
:rule-classes rule-classes
:instructions instructions
:hints hints
:otf-flg otf-flg
:event-name event-name
:doc doc)
where equiv1 and equiv2 are known equivalence relations, term is a
call of a function fn on the correct number of distinct variable
arguments (fn x1 ... xn), k is a positive integer less than or equal
to the arity of fn, and other arguments are as specified in the
documentation for defthm. The defcong macro expands into a call
of defthm. The name of the defthm event is
equiv1-implies-equiv2-fn-k unless an :event-name keyword argument is
supplied for the name. The term of the theorem is
(implies (equiv1 xk yk)
(equiv2 (fn x1... xk ...xn)
(fn x1... yk ...xn))).
The rule-class :congruence 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 keyword arguments above.