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Int+denv

Int+denv->int

Get the int field from a int+denv.

Signature
(int+denv->int x) → int
Arguments: x — Guard (int+denv-p x).
Returns: int — Type (integerp int).

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

Definitions and Theorems

Function: int+denv->int$inline

(defun int+denv->int$inline (x)
  (declare (xargs :guard (int+denv-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'int+denv->int))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (ifix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: integerp-of-int+denv->int

(defthm integerp-of-int+denv->int
  (b* ((int (int+denv->int$inline x)))
    (integerp int))
  :rule-classes :rewrite)

Theorem: int+denv->int$inline-of-int+denv-fix-x

(defthm int+denv->int$inline-of-int+denv-fix-x
  (equal (int+denv->int$inline (int+denv-fix x))
         (int+denv->int$inline x)))

Theorem: int+denv->int$inline-int+denv-equiv-congruence-on-x

(defthm int+denv->int$inline-int+denv-equiv-congruence-on-x
  (implies (int+denv-equiv x x-equiv)
           (equal (int+denv->int$inline x)
                  (int+denv->int$inline x-equiv)))
  :rule-classes :congruence)