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Undocumented

Fgl-ev-congruence-rulelist-correct-p

(fgl-ev-congruence-rulelist-correct-p x) recognizes lists where every element satisfies fgl-ev-congruence-rule-correct-p.

Signature
(fgl-ev-congruence-rulelist-correct-p x) → std::bool

This is an ordinary deflist. It is "loose" in that it does not care whether x is nil-terminated.

Definitions and Theorems

Function: fgl-ev-congruence-rulelist-correct-p

(defun fgl-ev-congruence-rulelist-correct-p (x)
  (declare (xargs :guard (congruence-rulelist-p x)))
  (let ((__function__ 'fgl-ev-congruence-rulelist-correct-p))
    (declare (ignorable __function__))
    (if (consp x)
        (and (fgl-ev-congruence-rule-correct-p (car x))
             (fgl-ev-congruence-rulelist-correct-p (cdr x)))
      t)))

Theorem: fgl-ev-congruence-rulelist-correct-p-of-congruence-rulelist-fix-x

(defthm
  fgl-ev-congruence-rulelist-correct-p-of-congruence-rulelist-fix-x
 (equal
  (fgl-ev-congruence-rulelist-correct-p (congruence-rulelist-fix x))
  (fgl-ev-congruence-rulelist-correct-p x)))

Theorem: fgl-ev-congruence-rulelist-correct-p-congruence-rulelist-equiv-congruence-on-x

(defthm
 fgl-ev-congruence-rulelist-correct-p-congruence-rulelist-equiv-congruence-on-x
 (implies (congruence-rulelist-equiv x x-equiv)
          (equal (fgl-ev-congruence-rulelist-correct-p x)
                 (fgl-ev-congruence-rulelist-correct-p x-equiv)))
 :rule-classes :congruence)

Subtopics

Fgl-ev-congruence-rulelist-correct-p-basics: Basic theorems about fgl-ev-congruence-rulelist-correct-p, generated by deflist.