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• Truth

Depends-on

Signature

(depends-on n truth numvars) → *

Arguments

n — Guard (natp n).

truth — Guard (integerp truth).

numvars — Guard (natp numvars).

Definitions and Theorems

Function: depends-on

(defun depends-on (n truth numvars)
  (declare (xargs :guard (and (natp n)
                              (integerp truth)
                              (natp numvars))))
  (declare (xargs :guard (< n numvars)))
  (let ((__function__ 'depends-on))
    (declare (ignorable __function__))
    (b* ((var (var n numvars))
         (truth (truth-norm truth numvars)))
      (not (equal (logand (lognot var) truth)
                  (ash (logand var truth)
                       (- (ash 1 (lnfix n)))))))))

Theorem: depends-on-of-truth-norm

(defthm depends-on-of-truth-norm
  (equal (depends-on n (truth-norm truth numvars)
                     numvars)
         (depends-on n truth numvars)))

Theorem: depends-on-correct

(defthm depends-on-correct
  (implies (and (not (depends-on n truth numvars))
                (< (nfix n) (nfix numvars)))
           (equal (truth-eval truth (env-update n val env)
                              numvars)
                  (truth-eval truth env numvars))))

Theorem: depends-on-of-nfix-n

(defthm depends-on-of-nfix-n
  (equal (depends-on (nfix n) truth numvars)
         (depends-on n truth numvars)))

Theorem: depends-on-nat-equiv-congruence-on-n

(defthm depends-on-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (depends-on n truth numvars)
                  (depends-on n-equiv truth numvars)))
  :rule-classes :congruence)

Theorem: depends-on-of-ifix-truth

(defthm depends-on-of-ifix-truth
  (equal (depends-on n (ifix truth) numvars)
         (depends-on n truth numvars)))

Theorem: depends-on-int-equiv-congruence-on-truth

(defthm depends-on-int-equiv-congruence-on-truth
  (implies (int-equiv truth truth-equiv)
           (equal (depends-on n truth numvars)
                  (depends-on n truth-equiv numvars)))
  :rule-classes :congruence)

Theorem: depends-on-of-nfix-numvars

(defthm depends-on-of-nfix-numvars
  (equal (depends-on n truth (nfix numvars))
         (depends-on n truth numvars)))

Theorem: depends-on-nat-equiv-congruence-on-numvars

(defthm depends-on-nat-equiv-congruence-on-numvars
  (implies (nat-equiv numvars numvars-equiv)
           (equal (depends-on n truth numvars)
                  (depends-on n truth numvars-equiv)))
  :rule-classes :congruence)