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Context

Context-equiv

Basic equivalence relation for context structures.

Definitions and Theorems

Function: context-equiv$inline

(defun context-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (contextp acl2::x)
                              (contextp acl2::y))))
  (equal (context-fix acl2::x)
         (context-fix acl2::y)))

Theorem: context-equiv-is-an-equivalence

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

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

(defthm context-equiv-implies-equal-context-fix-1
  (implies (context-equiv acl2::x x-equiv)
           (equal (context-fix acl2::x)
                  (context-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: context-fix-under-context-equiv

(defthm context-fix-under-context-equiv
  (context-equiv (context-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-context-fix-1-forward-to-context-equiv
  (implies (equal (context-fix acl2::x) acl2::y)
           (context-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-context-fix-2-forward-to-context-equiv
  (implies (equal acl2::x (context-fix acl2::y))
           (context-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm context-equiv-of-context-fix-1-forward
  (implies (context-equiv (context-fix acl2::x)
                          acl2::y)
           (context-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm context-equiv-of-context-fix-2-forward
  (implies (context-equiv acl2::x (context-fix acl2::y))
           (context-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)