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Expr-label-addr

Expr-label-addr->arg

Get the arg field from a expr-label-addr.

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

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

Definitions and Theorems

Function: expr-label-addr->arg$inline

(defun expr-label-addr->arg$inline (x)
  (declare (xargs :guard (exprp x)))
  (declare (xargs :guard (equal (expr-kind x) :label-addr)))
  (mbe :logic
       (b* ((x (and (equal (expr-kind x) :label-addr)
                    x)))
         (ident-fix (cdr x)))
       :exec (cdr x)))

Theorem: identp-of-expr-label-addr->arg

(defthm identp-of-expr-label-addr->arg
  (b* ((arg (expr-label-addr->arg$inline x)))
    (identp arg))
  :rule-classes :rewrite)

Theorem: expr-label-addr->arg$inline-of-expr-fix-x

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

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

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

Theorem: expr-label-addr->arg-when-wrong-kind

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