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Proposals

Props-with-author+round

Retrieve, from a set of proposals, the subset of proposals with a given author and round.

Signature
(props-with-author+round author round props) → props-with-author+round
Arguments: author — Guard (addressp author).; round — Guard (posp round).; props — Guard (proposal-setp props).
Returns: props-with-author+round — Type (proposal-setp props-with-author+round).

Definitions and Theorems

Function: props-with-author+round

(defun props-with-author+round (author round props)
 (declare (xargs :guard (and (addressp author)
                             (posp round)
                             (proposal-setp props))))
 (let ((__function__ 'props-with-author+round))
  (declare (ignorable __function__))
  (b* (((when (emptyp (proposal-set-fix props)))
        nil)
       ((proposal prop) (head props)))
    (if (and (equal (address-fix author) prop.author)
             (equal (pos-fix round) prop.round))
        (insert (proposal-fix prop)
                (props-with-author+round author round (tail props)))
      (props-with-author+round author round (tail props))))))

Theorem: proposal-setp-of-props-with-author+round

(defthm proposal-setp-of-props-with-author+round
  (b* ((props-with-author+round
            (props-with-author+round author round props)))
    (proposal-setp props-with-author+round))
  :rule-classes :rewrite)

Theorem: props-with-author+round-subset

(defthm props-with-author+round-subset
  (implies (proposal-setp props)
           (b* ((?props-with-author+round
                     (props-with-author+round author round props)))
             (subset props-with-author+round props))))

Theorem: props-with-author+round-of-empty

(defthm props-with-author+round-of-empty
  (equal (props-with-author+round author round nil)
         nil))

Theorem: in-of-props-with-author+round

(defthm in-of-props-with-author+round
  (equal (in prop
             (props-with-author+round author round props))
         (and (in prop (proposal-set-fix props))
              (equal (proposal->author prop)
                     (address-fix author))
              (equal (proposal->round prop)
                     (pos-fix round)))))

Theorem: not-emptyp-of-props-with-author+round

(defthm not-emptyp-of-props-with-author+round
  (implies
       (and (in prop props)
            (proposal-setp props)
            (equal (proposal->author prop) author)
            (equal (proposal->round prop) round))
       (not (emptyp (props-with-author+round author round props)))))

Theorem: props-with-author+round-when-none-author

(defthm props-with-author+round-when-none-author
  (implies (prop-set-none-author-p author props)
           (equal (props-with-author+round author round props)
                  nil)))

Theorem: props-with-author+round-of-address-fix-author

(defthm props-with-author+round-of-address-fix-author
  (equal (props-with-author+round (address-fix author)
                                  round props)
         (props-with-author+round author round props)))

Theorem: props-with-author+round-address-equiv-congruence-on-author

(defthm props-with-author+round-address-equiv-congruence-on-author
  (implies
       (address-equiv author author-equiv)
       (equal (props-with-author+round author round props)
              (props-with-author+round author-equiv round props)))
  :rule-classes :congruence)

Theorem: props-with-author+round-of-pos-fix-round

(defthm props-with-author+round-of-pos-fix-round
  (equal (props-with-author+round author (pos-fix round)
                                  props)
         (props-with-author+round author round props)))

Theorem: props-with-author+round-pos-equiv-congruence-on-round

(defthm props-with-author+round-pos-equiv-congruence-on-round
  (implies
       (acl2::pos-equiv round round-equiv)
       (equal (props-with-author+round author round props)
              (props-with-author+round author round-equiv props)))
  :rule-classes :congruence)

Theorem: props-with-author+round-of-proposal-set-fix-props

(defthm props-with-author+round-of-proposal-set-fix-props
 (equal
     (props-with-author+round author round (proposal-set-fix props))
     (props-with-author+round author round props)))

Theorem: props-with-author+round-proposal-set-equiv-congruence-on-props

(defthm
     props-with-author+round-proposal-set-equiv-congruence-on-props
  (implies
       (proposal-set-equiv props props-equiv)
       (equal (props-with-author+round author round props)
              (props-with-author+round author round props-equiv)))
  :rule-classes :congruence)