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• Alias-norm.lisp

Lhatom-bound-fix

Signature

(lhatom-bound-fix bound offset x) → xx

Arguments

bound — Guard (integerp bound).

offset — Guard (natp offset).

x — Guard (lhatom-p x).

Returns

xx — Type (and (lhatom-p xx) (lhatom-normorderedp bound offset xx)).

Definitions and Theorems

Function: lhatom-bound-fix

(defun lhatom-bound-fix (bound offset x)
  (declare (xargs :guard (and (integerp bound)
                              (natp offset)
                              (lhatom-p x))))
  (declare (xargs :guard (lhatom-normorderedp bound offset x)))
  (let ((__function__ 'lhatom-bound-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (lhatom-normorderedp bound offset x)
             (lhatom-fix x)
           (lhatom-z))
         :exec x)))

Theorem: return-type-of-lhatom-bound-fix

(defthm return-type-of-lhatom-bound-fix
  (b* ((xx (lhatom-bound-fix bound offset x)))
    (and (lhatom-p xx)
         (lhatom-normorderedp bound offset xx)))
  :rule-classes :rewrite)

Theorem: lhatom-bound-fix-of-ifix-bound

(defthm lhatom-bound-fix-of-ifix-bound
  (equal (lhatom-bound-fix (ifix bound) offset x)
         (lhatom-bound-fix bound offset x)))

Theorem: lhatom-bound-fix-int-equiv-congruence-on-bound

(defthm lhatom-bound-fix-int-equiv-congruence-on-bound
  (implies (int-equiv bound bound-equiv)
           (equal (lhatom-bound-fix bound offset x)
                  (lhatom-bound-fix bound-equiv offset x)))
  :rule-classes :congruence)

Theorem: lhatom-bound-fix-of-nfix-offset

(defthm lhatom-bound-fix-of-nfix-offset
  (equal (lhatom-bound-fix bound (nfix offset) x)
         (lhatom-bound-fix bound offset x)))

Theorem: lhatom-bound-fix-nat-equiv-congruence-on-offset

(defthm lhatom-bound-fix-nat-equiv-congruence-on-offset
  (implies (nat-equiv offset offset-equiv)
           (equal (lhatom-bound-fix bound offset x)
                  (lhatom-bound-fix bound offset-equiv x)))
  :rule-classes :congruence)

Theorem: lhatom-bound-fix-of-lhatom-fix-x

(defthm lhatom-bound-fix-of-lhatom-fix-x
  (equal (lhatom-bound-fix bound offset (lhatom-fix x))
         (lhatom-bound-fix bound offset x)))

Theorem: lhatom-bound-fix-lhatom-equiv-congruence-on-x

(defthm lhatom-bound-fix-lhatom-equiv-congruence-on-x
  (implies (lhatom-equiv x x-equiv)
           (equal (lhatom-bound-fix bound offset x)
                  (lhatom-bound-fix bound offset x-equiv)))
  :rule-classes :congruence)

Theorem: lhatom-bound-fix-when-lhatom-normorderedp

(defthm lhatom-bound-fix-when-lhatom-normorderedp
  (implies (lhatom-normorderedp bound offset x)
           (equal (lhatom-bound-fix bound offset x)
                  (lhatom-fix x))))

Theorem: lhatom-bound-fix-forward-to-normorderedp

(defthm lhatom-bound-fix-forward-to-normorderedp
  (lhatom-normorderedp bound
                       idx (lhatom-bound-fix bound idx x))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((lhatom-bound-fix bound idx x)))))

Theorem: lhatom-vars-of-lhatom-bound-fix

(defthm lhatom-vars-of-lhatom-bound-fix
  (implies (not (member v (lhatom-vars x)))
           (not (member v
                        (lhatom-vars (lhatom-bound-fix b o x))))))