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Function-dinfo-option

Function-dinfo-option-fix

Fixing function for function-dinfo-option structures.

Signature
(function-dinfo-option-fix x) → new-x
Arguments: x — Guard (function-dinfo-optionp x).
Returns: new-x — Type (function-dinfo-optionp new-x).

Definitions and Theorems

Function: function-dinfo-option-fix$inline

(defun function-dinfo-option-fix$inline (x)
  (declare (xargs :guard (function-dinfo-optionp x)))
  (let ((__function__ 'function-dinfo-option-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (function-dinfo-fix x)))
                           fty::val)))
         :exec x)))

Theorem: function-dinfo-optionp-of-function-dinfo-option-fix

(defthm function-dinfo-optionp-of-function-dinfo-option-fix
  (b* ((new-x (function-dinfo-option-fix$inline x)))
    (function-dinfo-optionp new-x))
  :rule-classes :rewrite)

Theorem: function-dinfo-option-fix-when-function-dinfo-optionp

(defthm function-dinfo-option-fix-when-function-dinfo-optionp
  (implies (function-dinfo-optionp x)
           (equal (function-dinfo-option-fix x)
                  x)))

Function: function-dinfo-option-equiv$inline

(defun function-dinfo-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (function-dinfo-optionp acl2::x)
                              (function-dinfo-optionp acl2::y))))
  (equal (function-dinfo-option-fix acl2::x)
         (function-dinfo-option-fix acl2::y)))

Theorem: function-dinfo-option-equiv-is-an-equivalence

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

Theorem: function-dinfo-option-equiv-implies-equal-function-dinfo-option-fix-1

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

Theorem: function-dinfo-option-fix-under-function-dinfo-option-equiv

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

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

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

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

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

Theorem: function-dinfo-option-equiv-of-function-dinfo-option-fix-1-forward

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

Theorem: function-dinfo-option-equiv-of-function-dinfo-option-fix-2-forward

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