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Step * 1 2 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))
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 ↓∈ as
⊢ ¬x ↓∈ [x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)]
BY
{ (RWO "bag-member-filter" 0 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))
7. bag-no-repeats(T;[x∈bag-remove-repeats(eq;bs)|¬bbag-deq-member(eq;x;as)])
8. x : T@i
9. x ↓∈ as
⊢ ¬(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))
6.  bag-no-repeats(T;bag-remove-repeats(eq;as))
7.  bag-no-repeats(T;[x\mmember{}bag-remove-repeats(eq;bs)|\mneg{}\msubb{}bag-deq-member(eq;x;as)])
8.  x  :  T@i
9.  x  \mdownarrow{}\mmember{}  as
\mvdash{}  \mneg{}x  \mdownarrow{}\mmember{}  [x\mmember{}bag-remove-repeats(eq;bs)|\mneg{}\msubb{}bag-deq-member(eq;x;as)]


By

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Latex:
(RWO  "bag-member-filter"  0  THEN  Auto)

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