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Proposals

Props-with-round

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

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

Definitions and Theorems

Function: props-with-round

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

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

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

Theorem: props-with-round-subset

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

Theorem: not-in-prop-set-when-none-with-round

(defthm not-in-prop-set-when-none-with-round
  (implies (and (emptyp (props-with-round (proposal->round prop)
                                          props))
                (proposal-setp props))
           (not (in prop props))))

Theorem: not-in-prop-subset-when-none-with-round

(defthm not-in-prop-subset-when-none-with-round
  (implies (and (emptyp (props-with-round (proposal->round prop)
                                          props))
                (subset props0 props)
                (proposal-setp props0)
                (proposal-setp props))
           (not (in prop props0))))

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

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

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

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

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

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

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

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