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Stmt-compound

Stmt-compound->stmt

Get the stmt field from a stmt-compound.

Signature
(stmt-compound->stmt x) → stmt
Arguments: x — Guard (stmtp x).
Returns: stmt — Type (comp-stmtp stmt).

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

Definitions and Theorems

Function: stmt-compound->stmt$inline

(defun stmt-compound->stmt$inline (x)
  (declare (xargs :guard (stmtp x)))
  (declare (xargs :guard (equal (stmt-kind x) :compound)))
  (mbe :logic
       (b* ((x (and (equal (stmt-kind x) :compound)
                    x)))
         (comp-stmt-fix (cdr x)))
       :exec (cdr x)))

Theorem: comp-stmtp-of-stmt-compound->stmt

(defthm comp-stmtp-of-stmt-compound->stmt
  (b* ((stmt (stmt-compound->stmt$inline x)))
    (comp-stmtp stmt))
  :rule-classes :rewrite)

Theorem: stmt-compound->stmt$inline-of-stmt-fix-x

(defthm stmt-compound->stmt$inline-of-stmt-fix-x
  (equal (stmt-compound->stmt$inline (stmt-fix x))
         (stmt-compound->stmt$inline x)))

Theorem: stmt-compound->stmt$inline-stmt-equiv-congruence-on-x

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

Theorem: stmt-compound->stmt-when-wrong-kind

(defthm stmt-compound->stmt-when-wrong-kind
  (implies (not (equal (stmt-kind x) :compound))
           (equal (stmt-compound->stmt x)
                  (comp-stmt-fix nil))))