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Step * 1 1 1 1 of Lemma bag-partitions-symmetry


1. T : Type
2. valueall-type(T)
3. eq : EqDecider(T)
4. bs : bag(T)
5. proddeq(bag-deq(eq);bag-deq(eq)) ∈ EqDecider(bag(T) × bag(T))
6. x : bag(T) × bag(T)
7. x ↓∈ bag-partitions(eq;bs)
8. (#x in bag-map(λp.<snd(p), fst(p)>;bag-partitions(eq;bs))) ~ (#<snd(x), fst(x)> in bag-partitions(eq;bs))
⊢ (#x in bag-to-set(proddeq(bag-deq(eq);bag-deq(eq));bag-splits(bs)))
= (#<snd(x), fst(x)> in bag-to-set(proddeq(bag-deq(eq);bag-deq(eq));bag-splits(bs)))
∈ ℤ
BY
{ ((BLemma `equal-count-bag-to-set` THENA Auto)
   THEN DVar `x'
   THEN Reduce 0
   THEN RWO "bag-member-splits" 0
   THEN Auto
   THEN RWO "bag-append-comm" 0
   THEN Auto)⋅ }

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Latex:

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Latex:

1.  T  :  Type
2.  valueall-type(T)
3.  eq  :  EqDecider(T)
4.  bs  :  bag(T)
5.  proddeq(bag-deq(eq);bag-deq(eq))  \mmember{}  EqDecider(bag(T)  \mtimes{}  bag(T))
6.  x  :  bag(T)  \mtimes{}  bag(T)
7.  x  \mdownarrow{}\mmember{}  bag-partitions(eq;bs)
8.  (\#x  in  bag-map(\mlambda{}p.<snd(p),  fst(p)>bag-partitions(eq;bs)))  \msim{}  (\#<snd(x),  fst(x)>  in  bag-partitions\000C(eq;bs))
\mvdash{}  (\#x  in  bag-to-set(proddeq(bag-deq(eq);bag-deq(eq));bag-splits(bs)))
=  (\#<snd(x),  fst(x)>  in  bag-to-set(proddeq(bag-deq(eq);bag-deq(eq));bag-splits(bs)))


By

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Latex:
((BLemma  `equal-count-bag-to-set`  THENA  Auto)
  THEN  DVar  `x'
  THEN  Reduce  0
  THEN  RWO  "bag-member-splits"  0
  THEN  Auto
  THEN  RWO  "bag-append-comm"  0
  THEN  Auto)\mcdot{}

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