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Decl/stmt-decl

Decl/stmt-decl->decl

Get the decl field from a decl/stmt-decl.

Signature
(decl/stmt-decl->decl x) → decl
Arguments: x — Guard (decl/stmt-p x).
Returns: decl — Type (declp decl).

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

Definitions and Theorems

Function: decl/stmt-decl->decl$inline

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

Theorem: declp-of-decl/stmt-decl->decl

(defthm declp-of-decl/stmt-decl->decl
  (b* ((decl (decl/stmt-decl->decl$inline x)))
    (declp decl))
  :rule-classes :rewrite)

Theorem: decl/stmt-decl->decl$inline-of-decl/stmt-fix-x

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

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

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

Theorem: decl/stmt-decl->decl-when-wrong-kind

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