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Cancel-parity-lits

Signature

(cancel-parity-lits x neg) → (mv negate new-x)

Arguments

x — literal-sorted.
    Guard (lit-listp x).

neg — Guard (bitp neg).

Returns

negate — Type (bitp negate).

new-x — Type (lit-listp new-x).

Definitions and Theorems

Function: cancel-parity-lits

(defun cancel-parity-lits (x neg)
  (declare (xargs :guard (and (lit-listp x) (bitp neg))))
  (let ((__function__ 'cancel-parity-lits))
    (declare (ignorable __function__))
    (b* (((when (or (atom x) (atom (cdr x))))
          (mv (lbfix neg) (lit-list-fix x)))
         (lit1 (lit-fix (car x)))
         ((when (eql lit1 1))
          (cancel-parity-lits (cdr x)
                              (b-not neg)))
         ((when (eql lit1 0))
          (cancel-parity-lits (cdr x) neg))
         (lit2 (lit-fix (cadr x)))
         ((when (eql lit1 lit2))
          (cancel-parity-lits (cddr x) neg))
         ((when (eql lit1 (lit-negate lit2)))
          (cancel-parity-lits (cddr x)
                              (b-not neg)))
         ((mv neg rest)
          (cancel-parity-lits (cdr x) neg)))
      (mv neg (cons lit1 rest)))))

Theorem: bitp-of-cancel-parity-lits.negate

(defthm bitp-of-cancel-parity-lits.negate
  (b* (((mv ?negate ?new-x)
        (cancel-parity-lits x neg)))
    (bitp negate))
  :rule-classes :type-prescription)

Theorem: lit-listp-of-cancel-parity-lits.new-x

(defthm lit-listp-of-cancel-parity-lits.new-x
  (b* (((mv ?negate ?new-x)
        (cancel-parity-lits x neg)))
    (lit-listp new-x))
  :rule-classes :rewrite)

Theorem: aignet-eval-parity-of-cancel-parity-lits

(defthm aignet-eval-parity-of-cancel-parity-lits
  (b* (((mv ?negate ?new-x)
        (cancel-parity-lits x neg)))
    (equal (aignet-eval-parity new-x invals regvals aignet)
           (b-xor (b-xor neg negate)
                  (aignet-eval-parity x invals regvals aignet)))))

Theorem: aignet-lit-listp-of-cancel-parity-lits

(defthm aignet-lit-listp-of-cancel-parity-lits
  (b* (((mv ?negate ?new-x)
        (cancel-parity-lits x neg)))
    (implies (aignet-lit-listp x aignet)
             (aignet-lit-listp new-x aignet))))

Theorem: cancel-parity-lits-of-lit-list-fix-x

(defthm cancel-parity-lits-of-lit-list-fix-x
  (equal (cancel-parity-lits (lit-list-fix x)
                             neg)
         (cancel-parity-lits x neg)))

Theorem: cancel-parity-lits-lit-list-equiv-congruence-on-x

(defthm cancel-parity-lits-lit-list-equiv-congruence-on-x
  (implies (satlink::lit-list-equiv x x-equiv)
           (equal (cancel-parity-lits x neg)
                  (cancel-parity-lits x-equiv neg)))
  :rule-classes :congruence)

Theorem: cancel-parity-lits-of-bfix-neg

(defthm cancel-parity-lits-of-bfix-neg
  (equal (cancel-parity-lits x (bfix neg))
         (cancel-parity-lits x neg)))

Theorem: cancel-parity-lits-bit-equiv-congruence-on-neg

(defthm cancel-parity-lits-bit-equiv-congruence-on-neg
  (implies (bit-equiv neg neg-equiv)
           (equal (cancel-parity-lits x neg)
                  (cancel-parity-lits x neg-equiv)))
  :rule-classes :congruence)