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Aliases-indexed->named-aux

Signature

(aliases-indexed->named-aux n aliases scope moddb indnamememo) 
  → 
(mv aliases1 indnamememo1)

Arguments

n — Guard (natp n).

scope — Guard (modscope-p scope).

moddb — Guard (moddb-ok moddb).

Returns

aliases1 — Type (equal (len aliases1) (len aliases)).

indnamememo1 — Type (equal (len indnamememo1) (len indnamememo)).

Definitions and Theorems

Function: aliases-indexed->named-aux

(defun
 aliases-indexed->named-aux
 (n aliases scope moddb indnamememo)
 (declare (xargs :stobjs (aliases moddb indnamememo)))
 (declare (xargs :guard (and (natp n)
                             (modscope-p scope)
                             (moddb-ok moddb))))
 (declare
  (xargs
   :guard
   (and (<= (lnfix n) (aliass-length aliases))
        (modscope-okp scope moddb)
        (aliases-boundedp-aux n aliases
                              (modscope-local-bound scope moddb)))))
 (let
  ((__function__ 'aliases-indexed->named-aux))
  (declare (ignorable __function__))
  (b*
     ((aliases (aliases-fix aliases))
      ((when (mbe :logic (zp (- (aliass-length aliases) (nfix n)))
                  :exec (eql (aliass-length aliases) n)))
       (mv aliases indnamememo))
      (lhs (get-alias n aliases))
      ((mv lhs1 indnamememo)
       (lhs-indexed->named lhs scope moddb indnamememo))
      (aliases (set-alias n lhs1 aliases)))
     (aliases-indexed->named-aux (1+ (lnfix n))
                                 aliases scope moddb indnamememo))))

Theorem: return-type-of-aliases-indexed->named-aux.aliases1

(defthm
 return-type-of-aliases-indexed->named-aux.aliases1
 (b*
  (((mv ?aliases1 ?indnamememo1)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))
  (equal (len aliases1) (len aliases)))
 :rule-classes :rewrite)

Theorem: return-type-of-aliases-indexed->named-aux.indnamememo1

(defthm
 return-type-of-aliases-indexed->named-aux.indnamememo1
 (b*
  (((mv ?aliases1 ?indnamememo1)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))
  (equal (len indnamememo1)
         (len indnamememo)))
 :rule-classes :rewrite)

Theorem: aliases-indexed->named-preserves-lesser-indices

(defthm
  aliases-indexed->named-preserves-lesser-indices
  (implies
       (< (nfix m) (nfix n))
       (equal (nth m
                   (mv-nth 0
                           (aliases-indexed->named-aux
                                n aliases scope moddb indnamememo)))
              (lhs-fix (nth m aliases)))))

Theorem: vars-of-aliases-indexed->named-aux

(defthm
 vars-of-aliases-indexed->named-aux
 (implies
  (and (<= (nfix n) (nfix m))
       (< (nfix m) (len aliases)))
  (svarlist-addr-p
     (lhs-vars
          (nth m
               (mv-nth 0
                       (aliases-indexed->named-aux
                            n aliases scope moddb indnamememo)))))))

Theorem: aliases-indexed->named-aux-of-nfix-n

(defthm
 aliases-indexed->named-aux-of-nfix-n
 (equal
    (aliases-indexed->named-aux (nfix n)
                                aliases scope moddb indnamememo)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))

Theorem: aliases-indexed->named-aux-nat-equiv-congruence-on-n

(defthm
 aliases-indexed->named-aux-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
      (aliases-indexed->named-aux n aliases scope moddb indnamememo)
      (aliases-indexed->named-aux n-equiv
                                  aliases scope moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-indexed->named-aux-of-lhslist-fix-aliases

(defthm
 aliases-indexed->named-aux-of-lhslist-fix-aliases
 (equal
    (aliases-indexed->named-aux n (lhslist-fix aliases)
                                scope moddb indnamememo)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))

Theorem: aliases-indexed->named-aux-lhslist-equiv-congruence-on-aliases

(defthm
 aliases-indexed->named-aux-lhslist-equiv-congruence-on-aliases
 (implies
  (lhslist-equiv aliases aliases-equiv)
  (equal
      (aliases-indexed->named-aux n aliases scope moddb indnamememo)
      (aliases-indexed->named-aux
           n
           aliases-equiv scope moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-indexed->named-aux-of-modscope-fix-scope

(defthm
 aliases-indexed->named-aux-of-modscope-fix-scope
 (equal
    (aliases-indexed->named-aux n aliases (modscope-fix scope)
                                moddb indnamememo)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))

Theorem: aliases-indexed->named-aux-modscope-equiv-congruence-on-scope

(defthm
 aliases-indexed->named-aux-modscope-equiv-congruence-on-scope
 (implies
  (modscope-equiv scope scope-equiv)
  (equal
      (aliases-indexed->named-aux n aliases scope moddb indnamememo)
      (aliases-indexed->named-aux
           n
           aliases scope-equiv moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-indexed->named-aux-of-moddb-fix-moddb

(defthm
 aliases-indexed->named-aux-of-moddb-fix-moddb
 (equal
    (aliases-indexed->named-aux n aliases scope (moddb-fix moddb)
                                indnamememo)
    (aliases-indexed->named-aux n aliases scope moddb indnamememo)))

Theorem: aliases-indexed->named-aux-moddb-equiv-congruence-on-moddb

(defthm
 aliases-indexed->named-aux-moddb-equiv-congruence-on-moddb
 (implies
  (moddb-equiv moddb moddb-equiv)
  (equal
      (aliases-indexed->named-aux n aliases scope moddb indnamememo)
      (aliases-indexed->named-aux
           n
           aliases scope moddb-equiv indnamememo)))
 :rule-classes :congruence)