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Declon/stmt-stmt

Declon/stmt-stmt->expr

Get the expr field from a declon/stmt-stmt.

Signature
(declon/stmt-stmt->expr x) → expr
Arguments: x — Guard (declon/stmt-p x).
Returns: expr — Type (exprp expr).

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

Definitions and Theorems

Function: declon/stmt-stmt->expr$inline

(defun declon/stmt-stmt->expr$inline (x)
  (declare (xargs :guard (declon/stmt-p x)))
  (declare (xargs :guard (equal (declon/stmt-kind x) :stmt)))
  (mbe :logic
       (b* ((x (and (equal (declon/stmt-kind x) :stmt)
                    x)))
         (expr-fix (cdr x)))
       :exec (cdr x)))

Theorem: exprp-of-declon/stmt-stmt->expr

(defthm exprp-of-declon/stmt-stmt->expr
  (b* ((expr (declon/stmt-stmt->expr$inline x)))
    (exprp expr))
  :rule-classes :rewrite)

Theorem: declon/stmt-stmt->expr$inline-of-declon/stmt-fix-x

(defthm declon/stmt-stmt->expr$inline-of-declon/stmt-fix-x
  (equal (declon/stmt-stmt->expr$inline (declon/stmt-fix x))
         (declon/stmt-stmt->expr$inline x)))

Theorem: declon/stmt-stmt->expr$inline-declon/stmt-equiv-congruence-on-x

(defthm
    declon/stmt-stmt->expr$inline-declon/stmt-equiv-congruence-on-x
  (implies (declon/stmt-equiv x x-equiv)
           (equal (declon/stmt-stmt->expr$inline x)
                  (declon/stmt-stmt->expr$inline x-equiv)))
  :rule-classes :congruence)

Theorem: declon/stmt-stmt->expr-when-wrong-kind

(defthm declon/stmt-stmt->expr-when-wrong-kind
  (implies (not (equal (declon/stmt-kind x) :stmt))
           (equal (declon/stmt-stmt->expr x)
                  (expr-fix nil))))