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Step * 1 2 of Lemma bag-parts-no-repeats


1. T : Type
2. valueall-type(T)
3. eq : EqDecider(T)
4. bs : bag(T)
5. ∀n:ℕ. ∀bs:bag(T).  ((#(bs) ≤ n) ⇒ bag-no-repeats(bag(T) List+;bag-parts(eq;bs)))
⊢ bag-no-repeats(bag(T) List+;bag-parts(eq;bs))
BY
{ (InstHyp [⌜#(bs)⌝;⌜bs⌝] (-1)⋅ 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.  \mforall{}n:\mBbbN{}.  \mforall{}bs:bag(T).    ((\#(bs)  \mleq{}  n)  {}\mRightarrow{}  bag-no-repeats(bag(T)  List\msupplus{};bag-parts(eq;bs)))
\mvdash{}  bag-no-repeats(bag(T)  List\msupplus{};bag-parts(eq;bs))


By

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Latex:
(InstHyp  [\mkleeneopen{}\#(bs)\mkleeneclose{};\mkleeneopen{}bs\mkleeneclose{}]  (-1)\mcdot{}  THEN  Auto)

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