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Initer-single

Initer-single->expr

Get the expr field from a initer-single.

Signature
(initer-single->expr x) → expr
Arguments: x — Guard (initerp x).
Returns: expr — Type (exprp expr).

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

Definitions and Theorems

Function: initer-single->expr$inline

(defun initer-single->expr$inline (x)
  (declare (xargs :guard (initerp x)))
  (declare (xargs :guard (equal (initer-kind x) :single)))
  (let ((__function__ 'initer-single->expr))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (initer-kind x) :single)
                      x)))
           (expr-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: exprp-of-initer-single->expr

(defthm exprp-of-initer-single->expr
  (b* ((expr (initer-single->expr$inline x)))
    (exprp expr))
  :rule-classes :rewrite)

Theorem: initer-single->expr$inline-of-initer-fix-x

(defthm initer-single->expr$inline-of-initer-fix-x
  (equal (initer-single->expr$inline (initer-fix x))
         (initer-single->expr$inline x)))

Theorem: initer-single->expr$inline-initer-equiv-congruence-on-x

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

Theorem: initer-single->expr-when-wrong-kind

(defthm initer-single->expr-when-wrong-kind
  (implies (not (equal (initer-kind x) :single))
           (equal (initer-single->expr x)
                  (expr-fix nil))))