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Boolean-value

Boolean-value->bool

Get the bool field from a boolean-value.

Signature
(boolean-value->bool x) → bool
Arguments: x — Guard (boolean-valuep x).
Returns: bool — Type (booleanp bool).

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

Definitions and Theorems

Function: boolean-value->bool$inline

(defun boolean-value->bool$inline (x)
  (declare (xargs :guard (boolean-valuep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'boolean-value->bool))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::bool-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: booleanp-of-boolean-value->bool

(defthm booleanp-of-boolean-value->bool
  (b* ((bool (boolean-value->bool$inline x)))
    (booleanp bool))
  :rule-classes :rewrite)

Theorem: boolean-value->bool$inline-of-boolean-value-fix-x

(defthm boolean-value->bool$inline-of-boolean-value-fix-x
  (equal (boolean-value->bool$inline (boolean-value-fix x))
         (boolean-value->bool$inline x)))

Theorem: boolean-value->bool$inline-boolean-value-equiv-congruence-on-x

(defthm
     boolean-value->bool$inline-boolean-value-equiv-congruence-on-x
  (implies (boolean-value-equiv x x-equiv)
           (equal (boolean-value->bool$inline x)
                  (boolean-value->bool$inline x-equiv)))
  :rule-classes :congruence)