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Svtv-concat->lhs

Signature

(svtv-concat->lhs x modidx moddb aliases) → (mv errs lhs)

Arguments

x — Guard (string-listp x).

modidx — Guard (natp modidx).

moddb — Guard (moddb-ok moddb).

Returns

lhs — Type (lhs-p lhs).

Definitions and Theorems

Function: svtv-concat->lhs

(defun svtv-concat->lhs (x modidx moddb aliases)
  (declare (xargs :stobjs (moddb aliases)))
  (declare (xargs :guard (and (string-listp x)
                              (natp modidx)
                              (moddb-ok moddb))))
  (declare
       (xargs :guard (svtv-mod-alias-guard modidx moddb aliases)))
  (let ((__function__ 'svtv-concat->lhs))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (mv nil nil))
         ((mv err1 first)
          (svtv-1wire->lhs (car x)
                           modidx moddb aliases))
         ((mv errs rest)
          (svtv-concat->lhs (cdr x)
                            modidx moddb aliases)))
      (if err1 (mv (cons err1 errs) nil)
        (mv errs (append first rest))))))

Theorem: lhs-p-of-svtv-concat->lhs.lhs

(defthm lhs-p-of-svtv-concat->lhs.lhs
  (b* (((mv ?errs ?lhs)
        (svtv-concat->lhs x modidx moddb aliases)))
    (lhs-p lhs))
  :rule-classes :rewrite)

Theorem: svtv-concat->lhs-of-string-list-fix-x

(defthm svtv-concat->lhs-of-string-list-fix-x
  (equal (svtv-concat->lhs (str::string-list-fix x)
                           modidx moddb aliases)
         (svtv-concat->lhs x modidx moddb aliases)))

Theorem: svtv-concat->lhs-string-list-equiv-congruence-on-x

(defthm svtv-concat->lhs-string-list-equiv-congruence-on-x
  (implies (str::string-list-equiv x x-equiv)
           (equal (svtv-concat->lhs x modidx moddb aliases)
                  (svtv-concat->lhs x-equiv modidx moddb aliases)))
  :rule-classes :congruence)

Theorem: svtv-concat->lhs-of-nfix-modidx

(defthm svtv-concat->lhs-of-nfix-modidx
  (equal (svtv-concat->lhs x (nfix modidx)
                           moddb aliases)
         (svtv-concat->lhs x modidx moddb aliases)))

Theorem: svtv-concat->lhs-nat-equiv-congruence-on-modidx

(defthm svtv-concat->lhs-nat-equiv-congruence-on-modidx
  (implies (nat-equiv modidx modidx-equiv)
           (equal (svtv-concat->lhs x modidx moddb aliases)
                  (svtv-concat->lhs x modidx-equiv moddb aliases)))
  :rule-classes :congruence)

Theorem: svtv-concat->lhs-of-moddb-fix-moddb

(defthm svtv-concat->lhs-of-moddb-fix-moddb
  (equal (svtv-concat->lhs x modidx (moddb-fix moddb)
                           aliases)
         (svtv-concat->lhs x modidx moddb aliases)))

Theorem: svtv-concat->lhs-moddb-equiv-congruence-on-moddb

(defthm svtv-concat->lhs-moddb-equiv-congruence-on-moddb
  (implies (moddb-equiv moddb moddb-equiv)
           (equal (svtv-concat->lhs x modidx moddb aliases)
                  (svtv-concat->lhs x modidx moddb-equiv aliases)))
  :rule-classes :congruence)

Theorem: svtv-concat->lhs-of-lhslist-fix-aliases

(defthm svtv-concat->lhs-of-lhslist-fix-aliases
  (equal (svtv-concat->lhs x modidx moddb (lhslist-fix aliases))
         (svtv-concat->lhs x modidx moddb aliases)))

Theorem: svtv-concat->lhs-lhslist-equiv-congruence-on-aliases

(defthm svtv-concat->lhs-lhslist-equiv-congruence-on-aliases
  (implies (lhslist-equiv aliases aliases-equiv)
           (equal (svtv-concat->lhs x modidx moddb aliases)
                  (svtv-concat->lhs x modidx moddb aliases-equiv)))
  :rule-classes :congruence)