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• Function-option-name-lst

Function-option-name-lst-equiv

Basic equivalence relation for function-option-name-lst structures.

Definitions and Theorems

Function: function-option-name-lst-equiv$inline

(defun function-option-name-lst-equiv$inline (acl2::x acl2::y)
 (declare (xargs :guard (and (function-option-name-lst-p acl2::x)
                             (function-option-name-lst-p acl2::y))))
 (equal (function-option-name-lst-fix acl2::x)
        (function-option-name-lst-fix acl2::y)))

Theorem: function-option-name-lst-equiv-is-an-equivalence

(defthm function-option-name-lst-equiv-is-an-equivalence
  (and (booleanp (function-option-name-lst-equiv x y))
       (function-option-name-lst-equiv x x)
       (implies (function-option-name-lst-equiv x y)
                (function-option-name-lst-equiv y x))
       (implies (and (function-option-name-lst-equiv x y)
                     (function-option-name-lst-equiv y z))
                (function-option-name-lst-equiv x z)))
  :rule-classes (:equivalence))

Theorem: function-option-name-lst-equiv-implies-equal-function-option-name-lst-fix-1

(defthm
 function-option-name-lst-equiv-implies-equal-function-option-name-lst-fix-1
 (implies (function-option-name-lst-equiv acl2::x x-equiv)
          (equal (function-option-name-lst-fix acl2::x)
                 (function-option-name-lst-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: function-option-name-lst-fix-under-function-option-name-lst-equiv

(defthm
  function-option-name-lst-fix-under-function-option-name-lst-equiv
  (function-option-name-lst-equiv
       (function-option-name-lst-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-function-option-name-lst-fix-1-forward-to-function-option-name-lst-equiv

(defthm
 equal-of-function-option-name-lst-fix-1-forward-to-function-option-name-lst-equiv
 (implies (equal (function-option-name-lst-fix acl2::x)
                 acl2::y)
          (function-option-name-lst-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-function-option-name-lst-fix-2-forward-to-function-option-name-lst-equiv

(defthm
 equal-of-function-option-name-lst-fix-2-forward-to-function-option-name-lst-equiv
 (implies (equal acl2::x
                 (function-option-name-lst-fix acl2::y))
          (function-option-name-lst-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: function-option-name-lst-equiv-of-function-option-name-lst-fix-1-forward

(defthm
 function-option-name-lst-equiv-of-function-option-name-lst-fix-1-forward
 (implies (function-option-name-lst-equiv
               (function-option-name-lst-fix acl2::x)
               acl2::y)
          (function-option-name-lst-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: function-option-name-lst-equiv-of-function-option-name-lst-fix-2-forward

(defthm
 function-option-name-lst-equiv-of-function-option-name-lst-fix-2-forward
 (implies (function-option-name-lst-equiv
               acl2::x
               (function-option-name-lst-fix acl2::y))
          (function-option-name-lst-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)