		Search-engine friendly clone of the ACL2 documentation.

Programdecl

Programdecl->id

Get the id field from a programdecl.

Signature
(programdecl->id x) → id
Arguments: x — Guard (programdeclp x).
Returns: id — Type (programidp id).

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

Definitions and Theorems

Function: programdecl->id$inline

(defun programdecl->id$inline (x)
  (declare (xargs :guard (programdeclp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'programdecl->id))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (programid-fix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: programidp-of-programdecl->id

(defthm programidp-of-programdecl->id
  (b* ((id (programdecl->id$inline x)))
    (programidp id))
  :rule-classes :rewrite)

Theorem: programdecl->id$inline-of-programdecl-fix-x

(defthm programdecl->id$inline-of-programdecl-fix-x
  (equal (programdecl->id$inline (programdecl-fix x))
         (programdecl->id$inline x)))

Theorem: programdecl->id$inline-programdecl-equiv-congruence-on-x

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