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Var-tablep

Var-tablep-basics

Basic theorems about var-tablep, generated by std::deflist.

Definitions and Theorems

Theorem: var-tablep-of-cons

(defthm var-tablep-of-cons
  (implies (var-tablep acl2::x)
           (iff (var-tablep (cons acl2::a acl2::x))
                (var-table-scopep acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: var-tablep-of-singleton

(defthm var-tablep-of-singleton
  (iff (var-tablep (cons acl2::a nil))
       (var-table-scopep acl2::a))
  :rule-classes ((:rewrite)))

Theorem: var-tablep-of-cdr-when-var-tablep

(defthm var-tablep-of-cdr-when-var-tablep
  (implies (and (var-tablep (double-rewrite acl2::x))
                (consp (cdr acl2::x)))
           (var-tablep (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: var-tablep-when-not-consp

(defthm var-tablep-when-not-consp
  (implies (not (consp acl2::x))
           (not (var-tablep acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: var-tablep-implies-consp

(defthm var-tablep-implies-consp
  (implies (var-tablep acl2::x)
           (consp acl2::x))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((acl2::element-list-nonempty-p acl2::x)))))

Theorem: var-table-scopep-of-car-when-var-tablep

(defthm var-table-scopep-of-car-when-var-tablep
  (implies (var-tablep acl2::x)
           (var-table-scopep (car acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-var-tablep

(defthm true-listp-when-var-tablep
  (implies (var-tablep acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: var-tablep-of-append

(defthm var-tablep-of-append
  (implies (and (var-tablep acl2::a)
                (var-tablep acl2::b))
           (var-tablep (append acl2::a acl2::b)))
  :rule-classes ((:rewrite)))