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• Macro-info-option

Macro-info-option-fix

Fixing function for macro-info-option structures.

Signature

(macro-info-option-fix x) → new-x

Arguments

x — Guard (macro-info-optionp x).

Returns

new-x — Type (macro-info-optionp new-x).

Definitions and Theorems

Function: macro-info-option-fix$inline

(defun macro-info-option-fix$inline (x)
  (declare (xargs :guard (macro-info-optionp x)))
  (mbe :logic (cond ((not x) nil)
                    (t (b* ((fty::val (macro-info-fix x)))
                         fty::val)))
       :exec x))

Theorem: macro-info-optionp-of-macro-info-option-fix

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

Theorem: macro-info-option-fix-when-macro-info-optionp

(defthm macro-info-option-fix-when-macro-info-optionp
  (implies (macro-info-optionp x)
           (equal (macro-info-option-fix x) x)))

Function: macro-info-option-equiv$inline

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

Theorem: macro-info-option-equiv-is-an-equivalence

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

Theorem: macro-info-option-equiv-implies-equal-macro-info-option-fix-1

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

Theorem: macro-info-option-fix-under-macro-info-option-equiv

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

Theorem: equal-of-macro-info-option-fix-1-forward-to-macro-info-option-equiv

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

Theorem: equal-of-macro-info-option-fix-2-forward-to-macro-info-option-equiv

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

Theorem: macro-info-option-equiv-of-macro-info-option-fix-1-forward

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

Theorem: macro-info-option-equiv-of-macro-info-option-fix-2-forward

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

Theorem: macro-info-option-fix$inline-of-macro-info-option-fix-x

(defthm macro-info-option-fix$inline-of-macro-info-option-fix-x
  (equal (macro-info-option-fix$inline (macro-info-option-fix x))
         (macro-info-option-fix$inline x)))

Theorem: macro-info-option-fix$inline-macro-info-option-equiv-congruence-on-x

(defthm
 macro-info-option-fix$inline-macro-info-option-equiv-congruence-on-x
 (implies (macro-info-option-equiv x x-equiv)
          (equal (macro-info-option-fix$inline x)
                 (macro-info-option-fix$inline x-equiv)))
 :rule-classes :congruence)