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Fenv

Fenv-fix

Fixing function for fenv structures.

Signature
(fenv-fix x) → new-x
Arguments: x — Guard (fenvp x).
Returns: new-x — Type (fenvp new-x).

Definitions and Theorems

Function: fenv-fix$inline

(defun fenv-fix$inline (x)
 (declare (xargs :guard (fenvp x)))
 (let ((__function__ 'fenv-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((constants (const-fenv-fix (cdr (std::da-nth 0 (cdr x)))))
          (curve (curve-fix (cdr (std::da-nth 1 (cdr x))))))
       (cons :fenv (list (cons 'constants constants)
                         (cons 'curve curve))))
     :exec x)))

Theorem: fenvp-of-fenv-fix

(defthm fenvp-of-fenv-fix
  (b* ((new-x (fenv-fix$inline x)))
    (fenvp new-x))
  :rule-classes :rewrite)

Theorem: fenv-fix-when-fenvp

(defthm fenv-fix-when-fenvp
  (implies (fenvp x)
           (equal (fenv-fix x) x)))

Function: fenv-equiv$inline

(defun fenv-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (fenvp acl2::x) (fenvp acl2::y))))
  (equal (fenv-fix acl2::x)
         (fenv-fix acl2::y)))

Theorem: fenv-equiv-is-an-equivalence

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

Theorem: fenv-equiv-implies-equal-fenv-fix-1

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

Theorem: fenv-fix-under-fenv-equiv

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

Theorem: equal-of-fenv-fix-1-forward-to-fenv-equiv

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

Theorem: equal-of-fenv-fix-2-forward-to-fenv-equiv

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

Theorem: fenv-equiv-of-fenv-fix-1-forward

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

Theorem: fenv-equiv-of-fenv-fix-2-forward

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