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• Svex-env-extract

Svex-env-extract-aux

Signature

(svex-env-extract-aux keys env) → env1

Arguments

keys — Guard (svarlist-p keys).

env — Guard (svex-env-p env).

Returns

env1 — Type (svex-env-p env1).

Definitions and Theorems

Function: svex-env-extract-aux

(defun svex-env-extract-aux (keys env)
  (declare (xargs :guard (and (svarlist-p keys)
                              (svex-env-p env))))
  (let ((__function__ 'svex-env-extract-aux))
    (declare (ignorable __function__))
    (if (atom keys)
        nil
      (cons (cons (svar-fix (car keys))
                  (svex-env-fastlookup (car keys) env))
            (svex-env-extract-aux (cdr keys)
                                  env)))))

Theorem: svex-env-p-of-svex-env-extract-aux

(defthm svex-env-p-of-svex-env-extract-aux
  (b* ((env1 (svex-env-extract-aux keys env)))
    (svex-env-p env1))
  :rule-classes :rewrite)

Theorem: svex-env-extract-aux-of-svarlist-fix-keys

(defthm svex-env-extract-aux-of-svarlist-fix-keys
  (equal (svex-env-extract-aux (svarlist-fix keys)
                               env)
         (svex-env-extract-aux keys env)))

Theorem: svex-env-extract-aux-svarlist-equiv-congruence-on-keys

(defthm svex-env-extract-aux-svarlist-equiv-congruence-on-keys
  (implies (svarlist-equiv keys keys-equiv)
           (equal (svex-env-extract-aux keys env)
                  (svex-env-extract-aux keys-equiv env)))
  :rule-classes :congruence)

Theorem: svex-env-extract-aux-of-svex-env-fix-env

(defthm svex-env-extract-aux-of-svex-env-fix-env
  (equal (svex-env-extract-aux keys (svex-env-fix env))
         (svex-env-extract-aux keys env)))

Theorem: svex-env-extract-aux-svex-env-equiv-congruence-on-env

(defthm svex-env-extract-aux-svex-env-equiv-congruence-on-env
  (implies (svex-env-equiv env env-equiv)
           (equal (svex-env-extract-aux keys env)
                  (svex-env-extract-aux keys env-equiv)))
  :rule-classes :congruence)