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Rv32im-le-states

Xregs

Fixtype of the x registers for RV32IM little endian.

This is a list of 31 unsigned 32-bit integers, according to riscv::stat and riscv::stat-validp. Recall that x0 is always 0 and thus not explicitly modeled.

Definitions and Theorems

Function: xregs-equiv$inline

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

Theorem: xregs-equiv-is-an-equivalence

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

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

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

Theorem: xregs-fix-under-xregs-equiv

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

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

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

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

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

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

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

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

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

Subtopics

Xregsp: Recognizer for xregs.
Xregs-fix: Fixer for xregs.