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Lhs-add-namespace

Signature

(lhs-add-namespace namespace x) → xx

Arguments

namespace — Guard (name-p namespace).

x — Guard (lhs-p x).

Returns

xx — Type (and (lhs-p xx) (svarlist-addr-p (lhs-vars xx))).

Definitions and Theorems

Function: lhs-add-namespace

(defun lhs-add-namespace (namespace x)
 (declare (xargs :guard (and (name-p namespace) (lhs-p x))))
 (declare (xargs :guard (svarlist-addr-p (lhs-vars x))))
 (let ((__function__ 'lhs-add-namespace))
  (declare (ignorable __function__))
  (b* (((when (atom x)) nil)
       ((lhrange first) (lhrange-fix (car x))))
   (cons
    (lhatom-case
     first.atom
     :z first
     :var
     (change-lhrange
        first
        :atom
        (change-lhatom-var
             first.atom
             :name (svar-add-namespace namespace first.atom.name))))
    (lhs-add-namespace namespace (cdr x))))))

Theorem: return-type-of-lhs-add-namespace

(defthm return-type-of-lhs-add-namespace
  (b* ((xx (lhs-add-namespace namespace x)))
    (and (lhs-p xx)
         (svarlist-addr-p (lhs-vars xx))))
  :rule-classes :rewrite)

Theorem: lhs-add-namespace-of-name-fix-namespace

(defthm lhs-add-namespace-of-name-fix-namespace
  (equal (lhs-add-namespace (name-fix namespace)
                            x)
         (lhs-add-namespace namespace x)))

Theorem: lhs-add-namespace-name-equiv-congruence-on-namespace

(defthm lhs-add-namespace-name-equiv-congruence-on-namespace
  (implies (name-equiv namespace namespace-equiv)
           (equal (lhs-add-namespace namespace x)
                  (lhs-add-namespace namespace-equiv x)))
  :rule-classes :congruence)

Theorem: lhs-add-namespace-of-lhs-fix-x

(defthm lhs-add-namespace-of-lhs-fix-x
  (equal (lhs-add-namespace namespace (lhs-fix x))
         (lhs-add-namespace namespace x)))

Theorem: lhs-add-namespace-lhs-equiv-congruence-on-x

(defthm lhs-add-namespace-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-add-namespace namespace x)
                  (lhs-add-namespace namespace x-equiv)))
  :rule-classes :congruence)