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Immdeps-main

Vl-evatomlist-immdeps

Signature
(vl-evatomlist-immdeps x ans &key (ss 'ss) (ctx 'ctx)) → new-ans
Arguments: x — Guard (vl-evatomlist-p x).; ans — Guard (vl-immdeps-p ans).; ss — Guard (vl-scopestack-p ss).; ctx — Guard (acl2::any-p ctx).
Returns: new-ans — Type (vl-immdeps-p new-ans).

Definitions and Theorems

Function: vl-evatomlist-immdeps-fn

(defun vl-evatomlist-immdeps-fn (x ans ss ctx)
  (declare (xargs :guard (and (vl-evatomlist-p x)
                              (vl-immdeps-p ans)
                              (vl-scopestack-p ss)
                              (acl2::any-p ctx))))
  (let ((__function__ 'vl-evatomlist-immdeps))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (vl-immdeps-fix ans))
         (ans (vl-evatom-immdeps (car x) ans)))
      (vl-evatomlist-immdeps (cdr x) ans))))

Theorem: vl-immdeps-p-of-vl-evatomlist-immdeps

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: vl-evatomlist-immdeps-fn-of-identity-ctx

(defthm vl-evatomlist-immdeps-fn-of-identity-ctx
  (equal (vl-evatomlist-immdeps-fn x ans ss (identity ctx))
         (vl-evatomlist-immdeps-fn x ans ss ctx)))

Theorem: vl-evatomlist-immdeps-fn-equal-congruence-on-ctx

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