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• Function-specification

Function-specification-fix

Fixing function for function-specification structures.

Signature

(function-specification-fix x) → new-x

Arguments

x — Guard (function-specificationp x).

Returns

new-x — Type (function-specificationp new-x).

Definitions and Theorems

Function: function-specification-fix$inline

(defun function-specification-fix$inline (x)
 (declare (xargs :guard (function-specificationp x)))
 (let ((__function__ 'function-specification-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((name (identifier-fix (cdr (std::da-nth 0 x))))
      (functions (function-header-list-fix (cdr (std::da-nth 1 x))))
      (specifier (function-specifier-fix (cdr (std::da-nth 2 x)))))
     (list (cons 'name name)
           (cons 'functions functions)
           (cons 'specifier specifier)))
    :exec x)))

Theorem: function-specificationp-of-function-specification-fix

(defthm function-specificationp-of-function-specification-fix
  (b* ((new-x (function-specification-fix$inline x)))
    (function-specificationp new-x))
  :rule-classes :rewrite)

Theorem: function-specification-fix-when-function-specificationp

(defthm function-specification-fix-when-function-specificationp
  (implies (function-specificationp x)
           (equal (function-specification-fix x)
                  x)))

Function: function-specification-equiv$inline

(defun function-specification-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (function-specificationp acl2::x)
                              (function-specificationp acl2::y))))
  (equal (function-specification-fix acl2::x)
         (function-specification-fix acl2::y)))

Theorem: function-specification-equiv-is-an-equivalence

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

Theorem: function-specification-equiv-implies-equal-function-specification-fix-1

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

Theorem: function-specification-fix-under-function-specification-equiv

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

Theorem: equal-of-function-specification-fix-1-forward-to-function-specification-equiv

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

Theorem: equal-of-function-specification-fix-2-forward-to-function-specification-equiv

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

Theorem: function-specification-equiv-of-function-specification-fix-1-forward

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

Theorem: function-specification-equiv-of-function-specification-fix-2-forward

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