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Simpadd0-gin

Simpadd0-gin->const-new

Get the const-new field from a simpadd0-gin.

Signature
(simpadd0-gin->const-new x) → const-new
Arguments: x — Guard (simpadd0-ginp x).
Returns: const-new — Type (symbolp const-new).

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

Definitions and Theorems

Function: simpadd0-gin->const-new$inline

(defun simpadd0-gin->const-new$inline (x)
  (declare (xargs :guard (simpadd0-ginp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'simpadd0-gin->const-new))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::symbol-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: symbolp-of-simpadd0-gin->const-new

(defthm symbolp-of-simpadd0-gin->const-new
  (b* ((const-new (simpadd0-gin->const-new$inline x)))
    (symbolp const-new))
  :rule-classes :rewrite)

Theorem: simpadd0-gin->const-new$inline-of-simpadd0-gin-fix-x

(defthm simpadd0-gin->const-new$inline-of-simpadd0-gin-fix-x
  (equal (simpadd0-gin->const-new$inline (simpadd0-gin-fix x))
         (simpadd0-gin->const-new$inline x)))

Theorem: simpadd0-gin->const-new$inline-simpadd0-gin-equiv-congruence-on-x

(defthm
  simpadd0-gin->const-new$inline-simpadd0-gin-equiv-congruence-on-x
  (implies (simpadd0-gin-equiv x x-equiv)
           (equal (simpadd0-gin->const-new$inline x)
                  (simpadd0-gin->const-new$inline x-equiv)))
  :rule-classes :congruence)