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• Namelist

Namelist-equiv

Basic equivalence relation for namelist structures.

Definitions and Theorems

Function: namelist-equiv$inline

(defun namelist-equiv$inline (x y)
  (declare (xargs :guard (and (namelist-p x) (namelist-p y))))
  (equal (namelist-fix x)
         (namelist-fix y)))

Theorem: namelist-equiv-is-an-equivalence

(defthm namelist-equiv-is-an-equivalence
  (and (booleanp (namelist-equiv x y))
       (namelist-equiv x x)
       (implies (namelist-equiv x y)
                (namelist-equiv y x))
       (implies (and (namelist-equiv x y)
                     (namelist-equiv y z))
                (namelist-equiv x z)))
  :rule-classes (:equivalence))

Theorem: namelist-equiv-implies-equal-namelist-fix-1

(defthm namelist-equiv-implies-equal-namelist-fix-1
  (implies (namelist-equiv x x-equiv)
           (equal (namelist-fix x)
                  (namelist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: namelist-fix-under-namelist-equiv

(defthm namelist-fix-under-namelist-equiv
  (namelist-equiv (namelist-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-namelist-fix-1-forward-to-namelist-equiv

(defthm equal-of-namelist-fix-1-forward-to-namelist-equiv
  (implies (equal (namelist-fix x) y)
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-namelist-fix-2-forward-to-namelist-equiv

(defthm equal-of-namelist-fix-2-forward-to-namelist-equiv
  (implies (equal x (namelist-fix y))
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: namelist-equiv-of-namelist-fix-1-forward

(defthm namelist-equiv-of-namelist-fix-1-forward
  (implies (namelist-equiv (namelist-fix x) y)
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: namelist-equiv-of-namelist-fix-2-forward

(defthm namelist-equiv-of-namelist-fix-2-forward
  (implies (namelist-equiv x (namelist-fix y))
           (namelist-equiv x y))
  :rule-classes :forward-chaining)