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Step * 1 1 2 of Lemma sub-bags-no-repeats


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({p:bag(T) × bag(T)| p ↓∈ bag-partitions(eq;bs)} ;bb)
BY
{ xxxAssert ⌜bag-no-repeats(bag(T) × bag(T);bb)⌝⋅xxx }

1
.....assertion..... 
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(T);bb)

2
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)} )
7. bag-no-repeats(bag(T) × bag(T);bb)
⊢ bag-no-repeats({p:bag(T) × bag(T)| p ↓∈ bag-partitions(eq;bs)} ;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)
5.  bb  :  bag(\{p:bag(T)  \mtimes{}  bag(T)|  p  \mdownarrow{}\mmember{}  bag-partitions(eq;bs)\}  )
6.  bag-partitions(eq;bs)  =  bb
\mvdash{}  bag-no-repeats(\{p:bag(T)  \mtimes{}  bag(T)|  p  \mdownarrow{}\mmember{}  bag-partitions(eq;bs)\}  ;bb)


By

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Latex:
xxxAssert  \mkleeneopen{}bag-no-repeats(bag(T)  \mtimes{}  bag(T);bb)\mkleeneclose{}\mcdot{}xxx

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