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• Tyname-info

Tyname-info-fix

Fixing function for tyname-info structures.

Signature

(tyname-info-fix x) → new-x

Arguments

x — Guard (tyname-infop x).

Returns

new-x — Type (tyname-infop new-x).

Definitions and Theorems

Function: tyname-info-fix$inline

(defun tyname-info-fix$inline (x)
  (declare (xargs :guard (tyname-infop x)))
  (mbe :logic
       (b* ((type (type-fix (cdr (std::da-nth 0 x)))))
         (list (cons 'type type)))
       :exec x))

Theorem: tyname-infop-of-tyname-info-fix

(defthm tyname-infop-of-tyname-info-fix
  (b* ((new-x (tyname-info-fix$inline x)))
    (tyname-infop new-x))
  :rule-classes :rewrite)

Theorem: tyname-info-fix-when-tyname-infop

(defthm tyname-info-fix-when-tyname-infop
  (implies (tyname-infop x)
           (equal (tyname-info-fix x) x)))

Function: tyname-info-equiv$inline

(defun tyname-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (tyname-infop acl2::x)
                              (tyname-infop acl2::y))))
  (equal (tyname-info-fix acl2::x)
         (tyname-info-fix acl2::y)))

Theorem: tyname-info-equiv-is-an-equivalence

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

Theorem: tyname-info-equiv-implies-equal-tyname-info-fix-1

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

Theorem: tyname-info-fix-under-tyname-info-equiv

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

Theorem: equal-of-tyname-info-fix-1-forward-to-tyname-info-equiv

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

Theorem: equal-of-tyname-info-fix-2-forward-to-tyname-info-equiv

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

Theorem: tyname-info-equiv-of-tyname-info-fix-1-forward

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

Theorem: tyname-info-equiv-of-tyname-info-fix-2-forward

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

Theorem: tyname-info-fix$inline-of-tyname-info-fix-x

(defthm tyname-info-fix$inline-of-tyname-info-fix-x
  (equal (tyname-info-fix$inline (tyname-info-fix x))
         (tyname-info-fix$inline x)))

Theorem: tyname-info-fix$inline-tyname-info-equiv-congruence-on-x

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