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Formula-indices

Collect indices of all identifiers used throughout a formula.

Signature

(formula-indices formula) → *

Arguments

formula — Guard (lit-list-listp formula).

Definitions and Theorems

Function: formula-indices

(defun formula-indices (formula)
  (declare (xargs :guard (lit-list-listp formula)))
  (let ((__function__ 'formula-indices))
    (declare (ignorable __function__))
    (if (atom formula)
        nil
      (append (clause-indices (car formula))
              (formula-indices (cdr formula))))))

Theorem: formula-indices-when-atom

(defthm formula-indices-when-atom
  (implies (atom formula)
           (equal (formula-indices formula) nil)))

Theorem: formula-indices-of-cons

(defthm formula-indices-of-cons
  (equal (formula-indices (cons clause formula))
         (append (clause-indices clause)
                 (formula-indices formula))))

Theorem: formula-indices-of-lit-list-list-fix-formula

(defthm formula-indices-of-lit-list-list-fix-formula
  (equal (formula-indices (lit-list-list-fix formula))
         (formula-indices formula)))

Theorem: formula-indices-lit-list-list-equiv-congruence-on-formula

(defthm formula-indices-lit-list-list-equiv-congruence-on-formula
  (implies (lit-list-list-equiv formula formula-equiv)
           (equal (formula-indices formula)
                  (formula-indices formula-equiv)))
  :rule-classes :congruence)