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Aliases-to-var-decl-map-aux

Signature

(aliases-to-var-decl-map-aux n aliases scope moddb indnamememo) 
  → 
indnamememo1

Arguments

n — Guard (natp n).

scope — Guard (modscope-p scope).

moddb — Guard (moddb-ok moddb).

Returns

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

Definitions and Theorems

Function: aliases-to-var-decl-map-aux

(defun aliases-to-var-decl-map-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-to-var-decl-map-aux))
  (declare (ignorable __function__))
  (b* (((when (mbe :logic (zp (- (aliass-length aliases) (nfix n)))
                   :exec (eql (aliass-length aliases) n)))
        indnamememo)
       (lhs (get-alias n aliases))
       (indnamememo
            (lhs-register-indnamememo lhs scope moddb indnamememo)))
    (aliases-to-var-decl-map-aux (1+ (lnfix n))
                                 aliases scope moddb indnamememo))))

Theorem: return-type-of-aliases-to-var-decl-map-aux

(defthm return-type-of-aliases-to-var-decl-map-aux
  (b* ((indnamememo1 (aliases-to-var-decl-map-aux
                          n aliases scope moddb indnamememo)))
    (equal (len indnamememo1)
           (len indnamememo)))
  :rule-classes :rewrite)

Theorem: aliases-to-var-decl-map-aux-of-nfix-n

(defthm aliases-to-var-decl-map-aux-of-nfix-n
 (equal
   (aliases-to-var-decl-map-aux (nfix n)
                                aliases scope moddb indnamememo)
   (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)))

Theorem: aliases-to-var-decl-map-aux-nat-equiv-congruence-on-n

(defthm aliases-to-var-decl-map-aux-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
     (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)
     (aliases-to-var-decl-map-aux n-equiv
                                  aliases scope moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-to-var-decl-map-aux-of-lhslist-fix-aliases

(defthm aliases-to-var-decl-map-aux-of-lhslist-fix-aliases
 (equal
   (aliases-to-var-decl-map-aux n (lhslist-fix aliases)
                                scope moddb indnamememo)
   (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)))

Theorem: aliases-to-var-decl-map-aux-lhslist-equiv-congruence-on-aliases

(defthm
    aliases-to-var-decl-map-aux-lhslist-equiv-congruence-on-aliases
 (implies
  (lhslist-equiv aliases aliases-equiv)
  (equal
     (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)
     (aliases-to-var-decl-map-aux
          n
          aliases-equiv scope moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-to-var-decl-map-aux-of-modscope-fix-scope

(defthm aliases-to-var-decl-map-aux-of-modscope-fix-scope
 (equal
   (aliases-to-var-decl-map-aux n aliases (modscope-fix scope)
                                moddb indnamememo)
   (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)))

Theorem: aliases-to-var-decl-map-aux-modscope-equiv-congruence-on-scope

(defthm
     aliases-to-var-decl-map-aux-modscope-equiv-congruence-on-scope
 (implies
  (modscope-equiv scope scope-equiv)
  (equal
     (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)
     (aliases-to-var-decl-map-aux
          n
          aliases scope-equiv moddb indnamememo)))
 :rule-classes :congruence)

Theorem: aliases-to-var-decl-map-aux-of-moddb-fix-moddb

(defthm aliases-to-var-decl-map-aux-of-moddb-fix-moddb
 (equal
   (aliases-to-var-decl-map-aux n aliases scope (moddb-fix moddb)
                                indnamememo)
   (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)))

Theorem: aliases-to-var-decl-map-aux-moddb-equiv-congruence-on-moddb

(defthm aliases-to-var-decl-map-aux-moddb-equiv-congruence-on-moddb
 (implies
  (moddb-equiv moddb moddb-equiv)
  (equal
     (aliases-to-var-decl-map-aux n aliases scope moddb indnamememo)
     (aliases-to-var-decl-map-aux
          n
          aliases scope moddb-equiv indnamememo)))
 :rule-classes :congruence)