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Expr-string-info

Expr-string-info-equiv

Basic equivalence relation for expr-string-info structures.

Definitions and Theorems

Function: expr-string-info-equiv$inline

(defun expr-string-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (expr-string-infop acl2::x)
                              (expr-string-infop acl2::y))))
  (equal (expr-string-info-fix acl2::x)
         (expr-string-info-fix acl2::y)))

Theorem: expr-string-info-equiv-is-an-equivalence

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

Theorem: expr-string-info-equiv-implies-equal-expr-string-info-fix-1

(defthm expr-string-info-equiv-implies-equal-expr-string-info-fix-1
  (implies (expr-string-info-equiv acl2::x x-equiv)
           (equal (expr-string-info-fix acl2::x)
                  (expr-string-info-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: expr-string-info-fix-under-expr-string-info-equiv

(defthm expr-string-info-fix-under-expr-string-info-equiv
  (expr-string-info-equiv (expr-string-info-fix acl2::x)
                          acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-expr-string-info-fix-1-forward-to-expr-string-info-equiv

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

Theorem: equal-of-expr-string-info-fix-2-forward-to-expr-string-info-equiv

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

Theorem: expr-string-info-equiv-of-expr-string-info-fix-1-forward

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

Theorem: expr-string-info-equiv-of-expr-string-info-fix-2-forward

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