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Expr-list-nocallsp

Expr-list-nocallsp-basics

Basic theorems about expr-list-nocallsp, generated by std::deflist.

Definitions and Theorems

Theorem: expr-list-nocallsp-of-cons

(defthm expr-list-nocallsp-of-cons
  (equal (expr-list-nocallsp (cons acl2::a acl2::x))
         (and (expr-nocallsp acl2::a)
              (expr-list-nocallsp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expr-list-nocallsp-of-cdr-when-expr-list-nocallsp

(defthm expr-list-nocallsp-of-cdr-when-expr-list-nocallsp
  (implies (expr-list-nocallsp (double-rewrite acl2::x))
           (expr-list-nocallsp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expr-list-nocallsp-when-not-consp

(defthm expr-list-nocallsp-when-not-consp
  (implies (not (consp acl2::x))
           (expr-list-nocallsp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: expr-nocallsp-of-car-when-expr-list-nocallsp

(defthm expr-nocallsp-of-car-when-expr-list-nocallsp
  (implies (expr-list-nocallsp acl2::x)
           (expr-nocallsp (car acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expr-list-nocallsp-of-append

(defthm expr-list-nocallsp-of-append
  (equal (expr-list-nocallsp (append acl2::a acl2::b))
         (and (expr-list-nocallsp acl2::a)
              (expr-list-nocallsp acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: expr-list-nocallsp-of-list-fix

(defthm expr-list-nocallsp-of-list-fix
  (equal (expr-list-nocallsp (list-fix acl2::x))
         (expr-list-nocallsp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: expr-list-nocallsp-of-rev

(defthm expr-list-nocallsp-of-rev
  (equal (expr-list-nocallsp (rev acl2::x))
         (expr-list-nocallsp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))