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Sdm-instruction-table-entry

Sdm-instruction-table-entry-equiv

Basic equivalence relation for sdm-instruction-table-entry structures.

Definitions and Theorems

Function: sdm-instruction-table-entry-equiv$inline

(defun sdm-instruction-table-entry-equiv$inline (x y)
  (declare (xargs :guard (and (sdm-instruction-table-entry-p x)
                              (sdm-instruction-table-entry-p y))))
  (equal (sdm-instruction-table-entry-fix x)
         (sdm-instruction-table-entry-fix y)))

Theorem: sdm-instruction-table-entry-equiv-is-an-equivalence

(defthm sdm-instruction-table-entry-equiv-is-an-equivalence
  (and (booleanp (sdm-instruction-table-entry-equiv x y))
       (sdm-instruction-table-entry-equiv x x)
       (implies (sdm-instruction-table-entry-equiv x y)
                (sdm-instruction-table-entry-equiv y x))
       (implies (and (sdm-instruction-table-entry-equiv x y)
                     (sdm-instruction-table-entry-equiv y z))
                (sdm-instruction-table-entry-equiv x z)))
  :rule-classes (:equivalence))

Theorem: sdm-instruction-table-entry-equiv-implies-equal-sdm-instruction-table-entry-fix-1

(defthm
 sdm-instruction-table-entry-equiv-implies-equal-sdm-instruction-table-entry-fix-1
 (implies (sdm-instruction-table-entry-equiv x x-equiv)
          (equal (sdm-instruction-table-entry-fix x)
                 (sdm-instruction-table-entry-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: sdm-instruction-table-entry-fix-under-sdm-instruction-table-entry-equiv

(defthm
 sdm-instruction-table-entry-fix-under-sdm-instruction-table-entry-equiv
 (sdm-instruction-table-entry-equiv
      (sdm-instruction-table-entry-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-sdm-instruction-table-entry-fix-1-forward-to-sdm-instruction-table-entry-equiv

(defthm
 equal-of-sdm-instruction-table-entry-fix-1-forward-to-sdm-instruction-table-entry-equiv
 (implies (equal (sdm-instruction-table-entry-fix x)
                 y)
          (sdm-instruction-table-entry-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-sdm-instruction-table-entry-fix-2-forward-to-sdm-instruction-table-entry-equiv

(defthm
 equal-of-sdm-instruction-table-entry-fix-2-forward-to-sdm-instruction-table-entry-equiv
 (implies (equal x (sdm-instruction-table-entry-fix y))
          (sdm-instruction-table-entry-equiv x y))
 :rule-classes :forward-chaining)

Theorem: sdm-instruction-table-entry-equiv-of-sdm-instruction-table-entry-fix-1-forward

(defthm
 sdm-instruction-table-entry-equiv-of-sdm-instruction-table-entry-fix-1-forward
 (implies (sdm-instruction-table-entry-equiv
               (sdm-instruction-table-entry-fix x)
               y)
          (sdm-instruction-table-entry-equiv x y))
 :rule-classes :forward-chaining)

Theorem: sdm-instruction-table-entry-equiv-of-sdm-instruction-table-entry-fix-2-forward

(defthm
 sdm-instruction-table-entry-equiv-of-sdm-instruction-table-entry-fix-2-forward
 (implies (sdm-instruction-table-entry-equiv
               x (sdm-instruction-table-entry-fix y))
          (sdm-instruction-table-entry-equiv x y))
 :rule-classes :forward-chaining)