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Fenv

Fenv-equiv

Basic equivalence relation for fenv structures.

Definitions and Theorems

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)