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Label-casexpr

Label-casexpr->expr

Get the expr field from a label-casexpr.

Signature
(label-casexpr->expr x) → expr
Arguments: x — Guard (labelp x).
Returns: expr — Type (const-exprp expr).

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

Definitions and Theorems

Function: label-casexpr->expr$inline

(defun label-casexpr->expr$inline (x)
  (declare (xargs :guard (labelp x)))
  (declare (xargs :guard (equal (label-kind x) :casexpr)))
  (mbe :logic
       (b* ((x (and (equal (label-kind x) :casexpr)
                    x)))
         (const-expr-fix (car (cdr x))))
       :exec (car (cdr x))))

Theorem: const-exprp-of-label-casexpr->expr

(defthm const-exprp-of-label-casexpr->expr
  (b* ((expr (label-casexpr->expr$inline x)))
    (const-exprp expr))
  :rule-classes :rewrite)

Theorem: label-casexpr->expr$inline-of-label-fix-x

(defthm label-casexpr->expr$inline-of-label-fix-x
  (equal (label-casexpr->expr$inline (label-fix x))
         (label-casexpr->expr$inline x)))

Theorem: label-casexpr->expr$inline-label-equiv-congruence-on-x

(defthm label-casexpr->expr$inline-label-equiv-congruence-on-x
  (implies (label-equiv x x-equiv)
           (equal (label-casexpr->expr$inline x)
                  (label-casexpr->expr$inline x-equiv)))
  :rule-classes :congruence)

Theorem: label-casexpr->expr-when-wrong-kind

(defthm label-casexpr->expr-when-wrong-kind
  (implies (not (equal (label-kind x) :casexpr))
           (equal (label-casexpr->expr x)
                  (const-expr-fix nil))))