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Aignet-id-fix

Fix an ID so that it is valid for the aignet.

Signature

(aignet-id-fix id aignet) → new-id

Arguments

id — Guard (natp id).

aignet — Guard (node-listp aignet).

Returns

new-id — Type (aignet-idp new-id aignet).

Definitions and Theorems

Function: aignet-id-fix

(defun aignet-id-fix (id aignet)
  (declare (xargs :guard (and (natp id) (node-listp aignet))))
  (let ((__function__ 'aignet-id-fix))
    (declare (ignorable __function__))
    (if (aignet-idp id aignet)
        (nfix id)
      0)))

Theorem: return-type-of-aignet-id-fix

(defthm return-type-of-aignet-id-fix
  (b* ((new-id (aignet-id-fix id aignet)))
    (aignet-idp new-id aignet))
  :rule-classes :rewrite)

Theorem: aignet-id-fix-when-aignet-idp

(defthm aignet-id-fix-when-aignet-idp
  (implies (aignet-idp id aignet)
           (equal (aignet-id-fix id aignet)
                  (nfix id))))

Theorem: aignet-id-fix-id-val-linear

(defthm aignet-id-fix-id-val-linear
  (<= (aignet-id-fix id aignet)
      (fanin-count aignet))
  :rule-classes :linear)

Theorem: aignet-id-fix-of-node-list-fix

(defthm aignet-id-fix-of-node-list-fix
  (equal (aignet-id-fix x (node-list-fix aignet))
         (aignet-id-fix x aignet)))

Theorem: aignet-id-fix-of-nfix-id

(defthm aignet-id-fix-of-nfix-id
  (equal (aignet-id-fix (nfix id) aignet)
         (aignet-id-fix id aignet)))

Theorem: aignet-id-fix-nat-equiv-congruence-on-id

(defthm aignet-id-fix-nat-equiv-congruence-on-id
  (implies (nat-equiv id id-equiv)
           (equal (aignet-id-fix id aignet)
                  (aignet-id-fix id-equiv aignet)))
  :rule-classes :congruence)

Theorem: aignet-id-fix-of-node-list-fix-aignet

(defthm aignet-id-fix-of-node-list-fix-aignet
  (equal (aignet-id-fix id (node-list-fix aignet))
         (aignet-id-fix id aignet)))

Theorem: aignet-id-fix-node-list-equiv-congruence-on-aignet

(defthm aignet-id-fix-node-list-equiv-congruence-on-aignet
  (implies (node-list-equiv aignet aignet-equiv)
           (equal (aignet-id-fix id aignet)
                  (aignet-id-fix id aignet-equiv)))
  :rule-classes :congruence)