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• Std/system/term-transformations

Conjoin-equalities

Build a conjunction of equalities with the given left-hand and right-hand sides.

Signature

(conjoin-equalities lefts rights) → term

Arguments

lefts — Guard (pseudo-term-listp lefts).

rights — Guard (pseudo-term-listp rights).

Returns

term — Type (pseudo-termp term), given the guard.

Definitions and Theorems

Function: conjoin-equalities-aux

(defun conjoin-equalities-aux (lefts rights)
  (declare (xargs :guard (and (pseudo-term-listp lefts)
                              (pseudo-term-listp rights))))
  (declare (xargs :guard (= (len lefts) (len rights))))
  (let ((__function__ 'conjoin-equalities-aux))
    (declare (ignorable __function__))
    (if (endp lefts)
        nil
      (cons (cons 'equal
                  (cons (car lefts)
                        (cons (car rights) 'nil)))
            (conjoin-equalities-aux (cdr lefts)
                                    (cdr rights))))))

Theorem: pseudo-term-listp-of-conjoin-equalities-aux

(defthm pseudo-term-listp-of-conjoin-equalities-aux
  (implies (and (pseudo-term-listp lefts)
                (pseudo-term-listp rights)
                (= (len lefts) (len rights)))
           (b* ((equalities (conjoin-equalities-aux lefts rights)))
             (pseudo-term-listp equalities)))
  :rule-classes :rewrite)

Function: conjoin-equalities

(defun conjoin-equalities (lefts rights)
  (declare (xargs :guard (and (pseudo-term-listp lefts)
                              (pseudo-term-listp rights))))
  (declare (xargs :guard (= (len lefts) (len rights))))
  (let ((__function__ 'conjoin-equalities))
    (declare (ignorable __function__))
    (conjoin (conjoin-equalities-aux lefts rights))))

Theorem: pseudo-termp-of-conjoin-equalities

(defthm pseudo-termp-of-conjoin-equalities
  (implies (and (pseudo-term-listp lefts)
                (pseudo-term-listp rights)
                (= (len lefts) (len rights)))
           (b* ((term (conjoin-equalities lefts rights)))
             (pseudo-termp term)))
  :rule-classes :rewrite)