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Step * 1 of Lemma sub-bags-no-repeats


1. T : Type
2. eq : EqDecider(T)
3. bs : bag(T)
4. valueall-type(T)
⊢ bag-no-repeats(bag(T);bag-map(λp.(fst(p));bag-partitions(eq;bs)))
BY
{ (GenConcl ⌜bag-partitions(eq;bs) = bb ∈ bag({p:bag(T) × bag(T)| p ↓∈ bag-partitions(eq;bs)} )⌝⋅ THEN Auto) }

1
1. T : Type
2. eq : EqDecider(T)
3. bs : bag(T)
4. valueall-type(T)
5. bb : bag({p:bag(T) × bag(T)| p ↓∈ bag-partitions(eq;bs)} )
6. bag-partitions(eq;bs) = bb ∈ bag({p:bag(T) × bag(T)| p ↓∈ bag-partitions(eq;bs)} )
⊢ bag-no-repeats(bag(T);bag-map(λp.(fst(p));bb))

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  bs  :  bag(T)
4.  valueall-type(T)
\mvdash{}  bag-no-repeats(bag(T);bag-map(\mlambda{}p.(fst(p));bag-partitions(eq;bs)))


By

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Latex:
(GenConcl  \mkleeneopen{}bag-partitions(eq;bs)  =  bb\mkleeneclose{}\mcdot{}  THEN  Auto)

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