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• Svtv-to-fsm-defs

Svex-envlists-agree

Signature

(svex-envlists-agree vars x y) → *

Arguments

vars — Guard (svarlist-p vars).

x — Guard (svex-envlist-p x).

y — Guard (svex-envlist-p y).

Definitions and Theorems

Function: svex-envlists-agree

(defun svex-envlists-agree (vars x y)
  (declare (xargs :guard (and (svarlist-p vars)
                              (svex-envlist-p x)
                              (svex-envlist-p y))))
  (let ((__function__ 'svex-envlists-agree))
    (declare (ignorable __function__))
    (if (atom x)
        (atom y)
      (and (consp y)
           (svex-envs-agree vars (car x) (car y))
           (svex-envlists-agree vars (cdr x)
                                (cdr y))))))

Theorem: svex-envs-agree-nth-when-svex-envlists-agree

(defthm svex-envs-agree-nth-when-svex-envlists-agree
  (implies (svex-envlists-agree vars x y)
           (svex-envs-agree vars (nth n x)
                            (nth n y))))

Theorem: svex-envlists-agree-of-append-vars

(defthm svex-envlists-agree-of-append-vars
  (iff (svex-envlists-agree (append vars1 vars2)
                            x y)
       (and (svex-envlists-agree vars1 x y)
            (svex-envlists-agree vars2 x y))))

Theorem: svex-envlists-agree-of-svarlist-fix-vars

(defthm svex-envlists-agree-of-svarlist-fix-vars
  (equal (svex-envlists-agree (svarlist-fix vars)
                              x y)
         (svex-envlists-agree vars x y)))

Theorem: svex-envlists-agree-svarlist-equiv-congruence-on-vars

(defthm svex-envlists-agree-svarlist-equiv-congruence-on-vars
  (implies (svarlist-equiv vars vars-equiv)
           (equal (svex-envlists-agree vars x y)
                  (svex-envlists-agree vars-equiv x y)))
  :rule-classes :congruence)

Theorem: svex-envlists-agree-of-svex-envlist-fix-x

(defthm svex-envlists-agree-of-svex-envlist-fix-x
  (equal (svex-envlists-agree vars (svex-envlist-fix x)
                              y)
         (svex-envlists-agree vars x y)))

Theorem: svex-envlists-agree-svex-envlist-equiv-congruence-on-x

(defthm svex-envlists-agree-svex-envlist-equiv-congruence-on-x
  (implies (svex-envlist-equiv x x-equiv)
           (equal (svex-envlists-agree vars x y)
                  (svex-envlists-agree vars x-equiv y)))
  :rule-classes :congruence)

Theorem: svex-envlists-agree-of-svex-envlist-fix-y

(defthm svex-envlists-agree-of-svex-envlist-fix-y
  (equal (svex-envlists-agree vars x (svex-envlist-fix y))
         (svex-envlists-agree vars x y)))

Theorem: svex-envlists-agree-svex-envlist-equiv-congruence-on-y

(defthm svex-envlists-agree-svex-envlist-equiv-congruence-on-y
  (implies (svex-envlist-equiv y y-equiv)
           (equal (svex-envlists-agree vars x y)
                  (svex-envlists-agree vars x y-equiv)))
  :rule-classes :congruence)