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• Svex-select

Svex-select-staticify-assignment

Signature

(svex-select-staticify-assignment x rhs lhs-var-value) 
  → 
(mv static-lhs static-rhs)

Arguments

x — Guard (svex-select-p x).

rhs — Guard (svex-p rhs).

lhs-var-value — Guard (svex-p lhs-var-value).

Returns

static-lhs — Type (svex-select-p static-lhs).

static-rhs — Type (svex-p static-rhs).

Definitions and Theorems

Function: svex-select-staticify-assignment

(defun svex-select-staticify-assignment (x rhs lhs-var-value)
 (declare (xargs :guard (and (svex-select-p x)
                             (svex-p rhs)
                             (svex-p lhs-var-value))))
 (let ((__function__ 'svex-select-staticify-assignment))
  (declare (ignorable __function__))
  (b* (((when (svex-select-staticp x))
        (mv (svex-select-fix x) (svex-fix rhs)))
       ((svex-select-part x)))
   (svex-select-staticify-assignment
    x.subexp
    (svcall
      partinst x.lsb (svex-int x.width)
      (svex-select-to-svex-with-substitution x.subexp lhs-var-value)
      rhs)
    lhs-var-value))))

Theorem: svex-select-p-of-svex-select-staticify-assignment.static-lhs

(defthm svex-select-p-of-svex-select-staticify-assignment.static-lhs
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (svex-select-p static-lhs))
  :rule-classes :rewrite)

Theorem: svex-p-of-svex-select-staticify-assignment.static-rhs

(defthm svex-p-of-svex-select-staticify-assignment.static-rhs
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (svex-p static-rhs))
  :rule-classes :rewrite)

Theorem: svex-select-staticify-assignment-lhs-staticp

(defthm svex-select-staticify-assignment-lhs-staticp
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (svex-select-staticp static-lhs)))

Theorem: svex-vars-of-svex-select-staticify-assignmane

(defthm svex-vars-of-svex-select-staticify-assignmane
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (implies (and (not (member v (svex-select-vars x)))
                  (not (member v (svex-vars rhs)))
                  (not (member v (svex-vars lhs-var-value))))
             (not (member v (svex-vars static-rhs))))))

Theorem: svex-select-vars-of-svex-select-staticify-assignment-lhs

(defthm svex-select-vars-of-svex-select-staticify-assignment-lhs
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (implies (not (equal v (svex-select-inner-var x)))
             (not (member v (svex-select-vars static-lhs))))))

Theorem: svex-select-inner-var-of-svex-select-staticify-assignment

(defthm svex-select-inner-var-of-svex-select-staticify-assignment
  (b* (((mv ?static-lhs ?static-rhs)
        (svex-select-staticify-assignment x rhs lhs-var-value)))
    (equal (svex-select-inner-var static-lhs)
           (svex-select-inner-var x))))

Theorem: svex-select-staticify-assignment-of-svex-select-fix-x

(defthm svex-select-staticify-assignment-of-svex-select-fix-x
  (equal (svex-select-staticify-assignment (svex-select-fix x)
                                           rhs lhs-var-value)
         (svex-select-staticify-assignment x rhs lhs-var-value)))

Theorem: svex-select-staticify-assignment-svex-select-equiv-congruence-on-x

(defthm
 svex-select-staticify-assignment-svex-select-equiv-congruence-on-x
 (implies
  (svex-select-equiv x x-equiv)
  (equal
      (svex-select-staticify-assignment x rhs lhs-var-value)
      (svex-select-staticify-assignment x-equiv rhs lhs-var-value)))
 :rule-classes :congruence)

Theorem: svex-select-staticify-assignment-of-svex-fix-rhs

(defthm svex-select-staticify-assignment-of-svex-fix-rhs
  (equal (svex-select-staticify-assignment x (svex-fix rhs)
                                           lhs-var-value)
         (svex-select-staticify-assignment x rhs lhs-var-value)))

Theorem: svex-select-staticify-assignment-svex-equiv-congruence-on-rhs

(defthm
      svex-select-staticify-assignment-svex-equiv-congruence-on-rhs
 (implies
  (svex-equiv rhs rhs-equiv)
  (equal
      (svex-select-staticify-assignment x rhs lhs-var-value)
      (svex-select-staticify-assignment x rhs-equiv lhs-var-value)))
 :rule-classes :congruence)

Theorem: svex-select-staticify-assignment-of-svex-fix-lhs-var-value

(defthm svex-select-staticify-assignment-of-svex-fix-lhs-var-value
 (equal
   (svex-select-staticify-assignment x rhs (svex-fix lhs-var-value))
   (svex-select-staticify-assignment x rhs lhs-var-value)))

Theorem: svex-select-staticify-assignment-svex-equiv-congruence-on-lhs-var-value

(defthm
 svex-select-staticify-assignment-svex-equiv-congruence-on-lhs-var-value
 (implies
  (svex-equiv lhs-var-value lhs-var-value-equiv)
  (equal
      (svex-select-staticify-assignment x rhs lhs-var-value)
      (svex-select-staticify-assignment x rhs lhs-var-value-equiv)))
 :rule-classes :congruence)