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Svex-override-lhs

Signature

(svex-override-lhs x override-test offset override-val assigns) 
  → 
assigns1

Arguments

x — Guard (lhs-p x).

override-test — Guard (svex-p override-test).

offset — Guard (natp offset).

override-val — Guard (svex-p override-val).

assigns — Guard (svex-alist-p assigns).

Returns

assigns1 — Type (svex-alist-p assigns1).

Definitions and Theorems

Function: svex-override-lhs

(defun svex-override-lhs (x override-test
                            offset override-val assigns)
 (declare (xargs :guard (and (lhs-p x)
                             (svex-p override-test)
                             (natp offset)
                             (svex-p override-val)
                             (svex-alist-p assigns))))
 (let ((__function__ 'svex-override-lhs))
  (declare (ignorable __function__))
  (b*
   (((mv first rest) (lhs-decomp x))
    ((unless first)
     (svex-alist-fix assigns))
    ((lhrange first) first)
    (assigns
         (svex-override-lhs rest
                            override-test (+ (lnfix offset) first.w)
                            override-val assigns)))
   (svex-override-lhrange first override-test
                          offset override-val assigns))))

Theorem: svex-alist-p-of-svex-override-lhs

(defthm svex-alist-p-of-svex-override-lhs
  (b* ((assigns1 (svex-override-lhs x override-test
                                    offset override-val assigns)))
    (svex-alist-p assigns1))
  :rule-classes :rewrite)

Theorem: vars-of-svex-override-lhs

(defthm vars-of-svex-override-lhs
  (b* ((assigns1 (svex-override-lhs x override-test
                                    offset override-val assigns)))
    (implies (and (not (member v (svex-alist-vars assigns)))
                  (not (member v (svex-vars override-test)))
                  (not (member v (svex-vars override-val))))
             (not (member v (svex-alist-vars assigns1)))))
  :rule-classes :rewrite)

Theorem: lookup-of-svex-override-lhs

(defthm lookup-of-svex-override-lhs
  (b* ((assigns1 (svex-override-lhs x override-test
                                    offset override-val assigns)))
    (implies (and (not (member v (lhs-vars x)))
                  (not (svex-lookup v assigns))
                  (svar-p v))
             (not (svex-lookup v assigns1))))
  :rule-classes :rewrite)

Theorem: svex-override-lhs-of-lhs-fix-x

(defthm svex-override-lhs-of-lhs-fix-x
  (equal (svex-override-lhs (lhs-fix x)
                            override-test
                            offset override-val assigns)
         (svex-override-lhs x override-test
                            offset override-val assigns)))

Theorem: svex-override-lhs-lhs-equiv-congruence-on-x

(defthm svex-override-lhs-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (svex-override-lhs x override-test
                                     offset override-val assigns)
                  (svex-override-lhs x-equiv override-test
                                     offset override-val assigns)))
  :rule-classes :congruence)

Theorem: svex-override-lhs-of-svex-fix-override-test

(defthm svex-override-lhs-of-svex-fix-override-test
  (equal (svex-override-lhs x (svex-fix override-test)
                            offset override-val assigns)
         (svex-override-lhs x override-test
                            offset override-val assigns)))

Theorem: svex-override-lhs-svex-equiv-congruence-on-override-test

(defthm svex-override-lhs-svex-equiv-congruence-on-override-test
  (implies (svex-equiv override-test override-test-equiv)
           (equal (svex-override-lhs x override-test
                                     offset override-val assigns)
                  (svex-override-lhs x override-test-equiv
                                     offset override-val assigns)))
  :rule-classes :congruence)

Theorem: svex-override-lhs-of-nfix-offset

(defthm svex-override-lhs-of-nfix-offset
  (equal (svex-override-lhs x override-test (nfix offset)
                            override-val assigns)
         (svex-override-lhs x override-test
                            offset override-val assigns)))

Theorem: svex-override-lhs-nat-equiv-congruence-on-offset

(defthm svex-override-lhs-nat-equiv-congruence-on-offset
 (implies
      (nat-equiv offset offset-equiv)
      (equal (svex-override-lhs x override-test
                                offset override-val assigns)
             (svex-override-lhs x override-test
                                offset-equiv override-val assigns)))
 :rule-classes :congruence)

Theorem: svex-override-lhs-of-svex-fix-override-val

(defthm svex-override-lhs-of-svex-fix-override-val
  (equal (svex-override-lhs x override-test
                            offset (svex-fix override-val)
                            assigns)
         (svex-override-lhs x override-test
                            offset override-val assigns)))

Theorem: svex-override-lhs-svex-equiv-congruence-on-override-val

(defthm svex-override-lhs-svex-equiv-congruence-on-override-val
 (implies
      (svex-equiv override-val override-val-equiv)
      (equal (svex-override-lhs x override-test
                                offset override-val assigns)
             (svex-override-lhs x override-test
                                offset override-val-equiv assigns)))
 :rule-classes :congruence)

Theorem: svex-override-lhs-of-svex-alist-fix-assigns

(defthm svex-override-lhs-of-svex-alist-fix-assigns
  (equal (svex-override-lhs x override-test offset
                            override-val (svex-alist-fix assigns))
         (svex-override-lhs x override-test
                            offset override-val assigns)))

Theorem: svex-override-lhs-svex-alist-equiv-congruence-on-assigns

(defthm svex-override-lhs-svex-alist-equiv-congruence-on-assigns
 (implies
      (svex-alist-equiv assigns assigns-equiv)
      (equal (svex-override-lhs x override-test
                                offset override-val assigns)
             (svex-override-lhs x override-test
                                offset override-val assigns-equiv)))
 :rule-classes :congruence)