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


1. T : Type
2. eq : EqDecider(T)
3. u : T
4. v : T List
5. ∀bs:bag(T). (bag-no-repeats(T;bs) ⇒ bag-no-repeats(T;bag-subtract(eq;bs;v)))
6. bs : bag(T)
7. bag-no-repeats(T;bs)
⊢ bag-no-repeats(T;bag-drop(eq;bs;u))
BY
{ ((InstLemma `bag-drop-property` [⌜T⌝;⌜eq⌝;⌜u⌝;⌜bs⌝]⋅ THENA Auto) THEN D (-1) THEN Auto) }

1
1. T : Type
2. eq : EqDecider(T)
3. u : T
4. v : T List
5. ∀bs:bag(T). (bag-no-repeats(T;bs) ⇒ bag-no-repeats(T;bag-subtract(eq;bs;v)))
6. bs : bag(T)
7. bag-no-repeats(T;bs)
8. bs = ({u} + bag-drop(eq;bs;u)) ∈ bag(T)
⊢ bag-no-repeats(T;bag-drop(eq;bs;u))

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  u  :  T
4.  v  :  T  List
5.  \mforall{}bs:bag(T).  (bag-no-repeats(T;bs)  {}\mRightarrow{}  bag-no-repeats(T;bag-subtract(eq;bs;v)))
6.  bs  :  bag(T)
7.  bag-no-repeats(T;bs)
\mvdash{}  bag-no-repeats(T;bag-drop(eq;bs;u))


By

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Latex:
((InstLemma  `bag-drop-property`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}eq\mkleeneclose{};\mkleeneopen{}u\mkleeneclose{};\mkleeneopen{}bs\mkleeneclose{}]\mcdot{}  THENA  Auto)  THEN  D  (-1)  THEN  Auto)

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