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• Truth

Truth-norm

Signature

(truth-norm truth numvars) → norm-truth

Arguments

truth — Guard (integerp truth).

numvars — Guard (natp numvars).

Definitions and Theorems

Function: truth-norm

(defun
     truth-norm (truth numvars)
     (declare (xargs :guard (and (integerp truth) (natp numvars))))
     (let ((__function__ 'truth-norm))
          (declare (ignorable __function__))
          (loghead (ash 1 (lnfix numvars))
                   truth)))

Theorem: truth-eval-of-truth-norm

(defthm truth-eval-of-truth-norm
        (b* nil
            (equal (truth-eval (truth-norm truth numvars)
                               env numvars)
                   (truth-eval truth env numvars))))

Theorem: truth-norm-of-truth-norm

(defthm truth-norm-of-truth-norm
        (b* nil
            (equal (truth-norm (truth-norm truth numvars)
                               numvars)
                   (truth-norm truth numvars))))

Theorem: size-of-truth-norm

(defthm size-of-truth-norm
        (b* ((?norm-truth (truth-norm truth numvars)))
            (implies (and (natp size)
                          (<= (ash 1 (nfix numvars)) size))
                     (unsigned-byte-p size norm-truth))))

Theorem: truth-eval-of-truth-norm-minus1

(defthm
   truth-eval-of-truth-norm-minus1
   (b* nil
       (implies (and (syntaxp (and (quotep truth) (quotep numvars)))
                     (equal truth (truth-norm -1 numvars)))
                (truth-eval truth env numvars))))

Theorem: truth-norm-of-ifix-truth

(defthm truth-norm-of-ifix-truth
        (equal (truth-norm (ifix truth) numvars)
               (truth-norm truth numvars)))

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

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

Theorem: truth-norm-of-nfix-numvars

(defthm truth-norm-of-nfix-numvars
        (equal (truth-norm truth (nfix numvars))
               (truth-norm truth numvars)))

Theorem: truth-norm-nat-equiv-congruence-on-numvars

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