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Const-fenv

Const-fenv-equiv

Basic equivalence relation for const-fenv structures.

Definitions and Theorems

Function: const-fenv-equiv$inline

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

Theorem: const-fenv-equiv-is-an-equivalence

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

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

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

Theorem: const-fenv-fix-under-const-fenv-equiv

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

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

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

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

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

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

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

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

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