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Denv

Denv->functions

Get the functions field from a denv.

Signature
(denv->functions x) → functions
Arguments: x — Guard (denvp x).
Returns: functions — Type (function-denvp functions).

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

Definitions and Theorems

Function: denv->functions$inline

(defun denv->functions$inline (x)
  (declare (xargs :guard (denvp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'denv->functions))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (function-denv-fix (cdr (std::da-nth 1 (cdr x)))))
         :exec (cdr (std::da-nth 1 (cdr x))))))

Theorem: function-denvp-of-denv->functions

(defthm function-denvp-of-denv->functions
  (b* ((functions (denv->functions$inline x)))
    (function-denvp functions))
  :rule-classes :rewrite)

Theorem: denv->functions$inline-of-denv-fix-x

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

Theorem: denv->functions$inline-denv-equiv-congruence-on-x

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