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• Alias-norm.lisp

Aliases-put-pairs

Signature

(aliases-put-pairs pairs aliases) → aliases1

Arguments

pairs — Guard (lhspairs-p pairs).

aliases — Guard (aliases-normorderedp aliases).

Returns

aliases1 — Type (aliases-normorderedp aliases1).

Definitions and Theorems

Function: aliases-put-pairs

(defun aliases-put-pairs (pairs aliases)
  (declare (xargs :stobjs (aliases)))
  (declare (xargs :guard (and (lhspairs-p pairs)
                              (aliases-normorderedp aliases))))
  (declare
       (xargs :guard (svarlist-boundedp (lhspairs-vars pairs)
                                        (aliass-length aliases))))
  (let ((__function__ 'aliases-put-pairs))
    (declare (ignorable __function__))
    (b* ((pairs (lhspairs-fix pairs))
         ((when (atom pairs))
          (aliases-bound-fix aliases))
         ((unless (mbt (consp (car pairs))))
          (aliases-put-pairs (cdr pairs) aliases))
         ((cons x y) (car pairs))
         (aliases (aliases-add-pair x y aliases)))
      (aliases-put-pairs (cdr pairs)
                         aliases))))

Theorem: aliases-normorderedp-of-aliases-put-pairs

(defthm aliases-normorderedp-of-aliases-put-pairs
  (b* ((aliases1 (aliases-put-pairs pairs aliases)))
    (aliases-normorderedp aliases1))
  :rule-classes :rewrite)

Theorem: aliases-put-pairs-of-lhspairs-fix-pairs

(defthm aliases-put-pairs-of-lhspairs-fix-pairs
  (equal (aliases-put-pairs (lhspairs-fix pairs)
                            aliases)
         (aliases-put-pairs pairs aliases)))

Theorem: aliases-put-pairs-lhspairs-equiv-congruence-on-pairs

(defthm aliases-put-pairs-lhspairs-equiv-congruence-on-pairs
  (implies (lhspairs-equiv pairs pairs-equiv)
           (equal (aliases-put-pairs pairs aliases)
                  (aliases-put-pairs pairs-equiv aliases)))
  :rule-classes :congruence)

Theorem: aliases-put-pairs-of-aliases-bound-fix-aliases

(defthm aliases-put-pairs-of-aliases-bound-fix-aliases
  (equal (aliases-put-pairs pairs (aliases-bound-fix aliases))
         (aliases-put-pairs pairs aliases)))

Theorem: aliases-put-pairs-aliases-equiv-congruence-on-aliases

(defthm aliases-put-pairs-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (aliases-put-pairs pairs aliases)
                  (aliases-put-pairs pairs aliases-equiv)))
  :rule-classes :congruence)

Theorem: len-of-aliases-put-pairs

(defthm len-of-aliases-put-pairs
  (implies (svarlist-boundedp (lhspairs-vars pairs)
                              (len aliases))
           (equal (len (aliases-put-pairs pairs aliases))
                  (len aliases))))