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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)