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Step * 1 of Lemma bag-remove-repeats-append


1. T : Type
2. as : bag(T)
3. bs : bag(T)
4. eq : EqDecider(T)
5. bag-no-repeats(T;bag-remove-repeats(eq;as + bs))
⊢ bag-no-repeats(T;bag-remove-repeats(eq;as) + [x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)])
BY
{ (BLemma `bag-no-repeats-append` THEN Auto THEN Try ((BLemma `bag-remove-repeats-no-repeats` THEN Auto))) }

1
1. T : Type
2. as : bag(T)
3. bs : bag(T)
4. eq : EqDecider(T)
5. bag-no-repeats(T;bag-remove-repeats(eq;as + bs))
6. bag-no-repeats(T;bag-remove-repeats(eq;as))
⊢ bag-no-repeats(T;[x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)])

2
1. T : Type
2. as : bag(T)
3. bs : bag(T)
4. eq : EqDecider(T)
5. bag-no-repeats(T;bag-remove-repeats(eq;as + bs))
6. bag-no-repeats(T;bag-remove-repeats(eq;as))
7. bag-no-repeats(T;[x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)])
8. x : T@i
9. x ↓∈ bag-remove-repeats(eq;as)@i
⊢ ¬x ↓∈ [x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)]

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Latex:

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Latex:

1.  T  :  Type
2.  as  :  bag(T)
3.  bs  :  bag(T)
4.  eq  :  EqDecider(T)
5.  bag-no-repeats(T;bag-remove-repeats(eq;as  +  bs))
\mvdash{}  bag-no-repeats(T;bag-remove-repeats(eq;as)
+  [x\mmember{}bag-remove-repeats(eq;bs)|\mneg{}\msubb{}bag-deq-member(eq;x;as)])


By

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Latex:
(BLemma  `bag-no-repeats-append`
  THEN  Auto
  THEN  Try  ((BLemma  `bag-remove-repeats-no-repeats`  THEN  Auto)))

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