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Immdeps-main

Vl-final-immdeps

Signature
(vl-final-immdeps x ans &key (ss 'ss)) → new-ans
Arguments: x — Guard (vl-final-p x).; ans — Guard (vl-immdeps-p ans).; ss — Guard (vl-scopestack-p ss).
Returns: new-ans — Type (vl-immdeps-p new-ans).

Definitions and Theorems

Function: vl-final-immdeps-fn

(defun vl-final-immdeps-fn (x ans ss)
  (declare (xargs :guard (and (vl-final-p x)
                              (vl-immdeps-p ans)
                              (vl-scopestack-p ss))))
  (let ((__function__ 'vl-final-immdeps))
    (declare (ignorable __function__))
    (b* ((x (vl-final-fix x))
         (ans (vl-immdeps-fix ans))
         (ss (vl-scopestack-fix ss)))
      (b* (((vl-final x)))
        (vl-stmt-immdeps x.stmt ans :ctx x)))))

Theorem: vl-immdeps-p-of-vl-final-immdeps

(defthm vl-immdeps-p-of-vl-final-immdeps
  (b* ((new-ans (vl-final-immdeps-fn x ans ss)))
    (vl-immdeps-p new-ans))
  :rule-classes :rewrite)

Theorem: vl-final-immdeps-fn-of-vl-final-fix-x

(defthm vl-final-immdeps-fn-of-vl-final-fix-x
  (equal (vl-final-immdeps-fn (vl-final-fix x)
                              ans ss)
         (vl-final-immdeps-fn x ans ss)))

Theorem: vl-final-immdeps-fn-vl-final-equiv-congruence-on-x

(defthm vl-final-immdeps-fn-vl-final-equiv-congruence-on-x
  (implies (vl-final-equiv x x-equiv)
           (equal (vl-final-immdeps-fn x ans ss)
                  (vl-final-immdeps-fn x-equiv ans ss)))
  :rule-classes :congruence)

Theorem: vl-final-immdeps-fn-of-vl-immdeps-fix-ans

(defthm vl-final-immdeps-fn-of-vl-immdeps-fix-ans
  (equal (vl-final-immdeps-fn x (vl-immdeps-fix ans)
                              ss)
         (vl-final-immdeps-fn x ans ss)))

Theorem: vl-final-immdeps-fn-vl-immdeps-equiv-congruence-on-ans

(defthm vl-final-immdeps-fn-vl-immdeps-equiv-congruence-on-ans
  (implies (vl-immdeps-equiv ans ans-equiv)
           (equal (vl-final-immdeps-fn x ans ss)
                  (vl-final-immdeps-fn x ans-equiv ss)))
  :rule-classes :congruence)

Theorem: vl-final-immdeps-fn-of-vl-scopestack-fix-ss

(defthm vl-final-immdeps-fn-of-vl-scopestack-fix-ss
  (equal (vl-final-immdeps-fn x ans (vl-scopestack-fix ss))
         (vl-final-immdeps-fn x ans ss)))

Theorem: vl-final-immdeps-fn-vl-scopestack-equiv-congruence-on-ss

(defthm vl-final-immdeps-fn-vl-scopestack-equiv-congruence-on-ss
  (implies (vl-scopestack-equiv ss ss-equiv)
           (equal (vl-final-immdeps-fn x ans ss)
                  (vl-final-immdeps-fn x ans ss-equiv)))
  :rule-classes :congruence)