		Search-engine friendly clone of the ACL2 documentation.

Expression-add

Expression-add->arg2

Get the arg2 field from a expression-add.

Signature
(expression-add->arg2 x) → arg2
Arguments: x — Guard (expressionp x).
Returns: arg2 — Type (expressionp arg2).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: expression-add->arg2$inline

(defun expression-add->arg2$inline (x)
  (declare (xargs :guard (expressionp x)))
  (declare (xargs :guard (equal (expression-kind x) :add)))
  (let ((__function__ 'expression-add->arg2))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (expression-kind x) :add)
                      x)))
           (expression-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: expressionp-of-expression-add->arg2

(defthm expressionp-of-expression-add->arg2
  (b* ((arg2 (expression-add->arg2$inline x)))
    (expressionp arg2))
  :rule-classes :rewrite)

Theorem: expression-add->arg2$inline-of-expression-fix-x

(defthm expression-add->arg2$inline-of-expression-fix-x
  (equal (expression-add->arg2$inline (expression-fix x))
         (expression-add->arg2$inline x)))

Theorem: expression-add->arg2$inline-expression-equiv-congruence-on-x

(defthm expression-add->arg2$inline-expression-equiv-congruence-on-x
  (implies (expression-equiv x x-equiv)
           (equal (expression-add->arg2$inline x)
                  (expression-add->arg2$inline x-equiv)))
  :rule-classes :congruence)

Theorem: expression-add->arg2-when-wrong-kind

(defthm expression-add->arg2-when-wrong-kind
  (implies (not (equal (expression-kind x) :add))
           (equal (expression-add->arg2 x)
                  (expression-fix nil))))