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Literal-bool

Literal-bool->val

Get the val field from a literal-bool.

Signature
(literal-bool->val x) → val
Arguments: x — Guard (literalp x).
Returns: val — Type (booleanp val).

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

Definitions and Theorems

Function: literal-bool->val$inline

(defun literal-bool->val$inline (x)
  (declare (xargs :guard (literalp x)))
  (declare (xargs :guard (equal (literal-kind x) :bool)))
  (let ((__function__ 'literal-bool->val))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (literal-kind x) :bool) x)))
           (acl2::bool-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: booleanp-of-literal-bool->val

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

Theorem: literal-bool->val$inline-of-literal-fix-x

(defthm literal-bool->val$inline-of-literal-fix-x
  (equal (literal-bool->val$inline (literal-fix x))
         (literal-bool->val$inline x)))

Theorem: literal-bool->val$inline-literal-equiv-congruence-on-x

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

Theorem: literal-bool->val-when-wrong-kind

(defthm literal-bool->val-when-wrong-kind
  (implies (not (equal (literal-kind x) :bool))
           (equal (literal-bool->val x)
                  (acl2::bool-fix nil))))