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Step * of Lemma no-repeats-bag-partitions

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)].
  bag-no-repeats(bag(T) × bag(T);bag-partitions(eq;bs)) supposing valueall-type(T)
BY
{ (Auto THEN Unfold `bag-partitions` 0 THEN CallByValueReduce 0) }

1
.....aux..... 
1. T : Type
2. eq : EqDecider(T)
3. bs : bag(T)
4. valueall-type(T)
⊢ has-valueall(bag-splits(bs))

2
1. T : Type
2. eq : EqDecider(T)
3. bs : bag(T)
4. valueall-type(T)
⊢ bag-no-repeats(bag(T) × bag(T);bag-to-set(proddeq(bag-deq(eq);bag-deq(eq));bag-splits(bs)))

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[bs:bag(T)].
    bag-no-repeats(bag(T)  \mtimes{}  bag(T);bag-partitions(eq;bs))  supposing  valueall-type(T)


By

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Latex:
(Auto  THEN  Unfold  `bag-partitions`  0  THEN  CallByValueReduce  0)

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