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Function-denv-option-some

Function-denv-option-some->get

Get the get field from a function-denv-option-some.

Signature
(function-denv-option-some->get x) → get
Arguments: x — Guard (function-denv-optionp x).
Returns: get — Type (function-denvp get).

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

Definitions and Theorems

Function: function-denv-option-some->get$inline

(defun function-denv-option-some->get$inline (x)
  (declare (xargs :guard (function-denv-optionp x)))
  (declare (xargs :guard (equal (function-denv-option-kind x)
                                :some)))
  (let ((__function__ 'function-denv-option-some->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (function-denv-option-kind x)
                             :some)
                      x)))
           (function-denv-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: function-denvp-of-function-denv-option-some->get

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

Theorem: function-denv-option-some->get$inline-of-function-denv-option-fix-x

(defthm
 function-denv-option-some->get$inline-of-function-denv-option-fix-x
 (equal (function-denv-option-some->get$inline
             (function-denv-option-fix x))
        (function-denv-option-some->get$inline x)))

Theorem: function-denv-option-some->get$inline-function-denv-option-equiv-congruence-on-x

(defthm
 function-denv-option-some->get$inline-function-denv-option-equiv-congruence-on-x
 (implies (function-denv-option-equiv x x-equiv)
          (equal (function-denv-option-some->get$inline x)
                 (function-denv-option-some->get$inline x-equiv)))
 :rule-classes :congruence)

Theorem: function-denv-option-some->get-when-wrong-kind

(defthm function-denv-option-some->get-when-wrong-kind
  (implies (not (equal (function-denv-option-kind x)
                       :some))
           (equal (function-denv-option-some->get x)
                  (function-denv-fix nil))))