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Congruence-rule

Congruence-rule-p

Recognizer for congruence-rule structures.

Signature
(congruence-rule-p x) → *

Definitions and Theorems

Function: congruence-rule-p

(defun congruence-rule-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'congruence-rule-p))
    (declare (ignorable __function__))
    (and (true-listp x)
         (eql (len x) 4)
         (b* ((equiv-req (std::da-nth 0 x))
              (fn (std::da-nth 1 x))
              (arg-contexts (std::da-nth 2 x))
              (arity (std::da-nth 3 x)))
           (and (pseudo-fnsym-p equiv-req)
                (pseudo-fnsym-p fn)
                (equiv-contextslist-p arg-contexts)
                (natp arity))))))

Theorem: consp-when-congruence-rule-p

(defthm consp-when-congruence-rule-p
  (implies (congruence-rule-p x)
           (consp x))
  :rule-classes :compound-recognizer)