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• Code-ensemble

Code-ensemble-equiv

Basic equivalence relation for code-ensemble structures.

Definitions and Theorems

Function: code-ensemble-equiv$inline

(defun code-ensemble-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (code-ensemblep acl2::x)
                              (code-ensemblep acl2::y))))
  (equal (code-ensemble-fix acl2::x)
         (code-ensemble-fix acl2::y)))

Theorem: code-ensemble-equiv-is-an-equivalence

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

Theorem: code-ensemble-equiv-implies-equal-code-ensemble-fix-1

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

Theorem: code-ensemble-fix-under-code-ensemble-equiv

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

Theorem: equal-of-code-ensemble-fix-1-forward-to-code-ensemble-equiv

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

Theorem: equal-of-code-ensemble-fix-2-forward-to-code-ensemble-equiv

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

Theorem: code-ensemble-equiv-of-code-ensemble-fix-1-forward

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

Theorem: code-ensemble-equiv-of-code-ensemble-fix-2-forward

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