		Search-engine friendly clone of the ACL2 documentation.

Expr-preinc

Expr-preinc->arg

Get the arg field from a expr-preinc.

Signature
(expr-preinc->arg x) → arg
Arguments: x — Guard (exprp x).
Returns: arg — Type (exprp arg).

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

Definitions and Theorems

Function: expr-preinc->arg$inline

(defun expr-preinc->arg$inline (x)
  (declare (xargs :guard (exprp x)))
  (declare (xargs :guard (equal (expr-kind x) :preinc)))
  (mbe :logic
       (b* ((x (and (equal (expr-kind x) :preinc) x)))
         (expr-fix (std::da-nth 0 (cdr x))))
       :exec (std::da-nth 0 (cdr x))))

Theorem: exprp-of-expr-preinc->arg

(defthm exprp-of-expr-preinc->arg
  (b* ((arg (expr-preinc->arg$inline x)))
    (exprp arg))
  :rule-classes :rewrite)

Theorem: expr-preinc->arg$inline-of-expr-fix-x

(defthm expr-preinc->arg$inline-of-expr-fix-x
  (equal (expr-preinc->arg$inline (expr-fix x))
         (expr-preinc->arg$inline x)))

Theorem: expr-preinc->arg$inline-expr-equiv-congruence-on-x

(defthm expr-preinc->arg$inline-expr-equiv-congruence-on-x
  (implies (expr-equiv x x-equiv)
           (equal (expr-preinc->arg$inline x)
                  (expr-preinc->arg$inline x-equiv)))
  :rule-classes :congruence)

Theorem: expr-preinc->arg-when-wrong-kind

(defthm expr-preinc->arg-when-wrong-kind
  (implies (not (equal (expr-kind x) :preinc))
           (equal (expr-preinc->arg x)
                  (expr-fix nil))))