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Step * 1 of Lemma bag-drop-property2


1. T : Type
2. eq : EqDecider(T)@i
3. x : T@i
4. bs : bag(T)@i
5. bs = ({x} + bag-drop(eq;bs;x)) ∈ bag(T)
6. bag-no-repeats(T;bs)@i
7. x ↓∈ bs@i
8. bs = ({x} + bag-drop(eq;bs;x)) ∈ bag(T)
⊢ bag-no-repeats(T;bag-drop(eq;bs;x))
BY
{ (BLemma `bag-drop-no-repeats` THEN Auto) }

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)@i
3.  x  :  T@i
4.  bs  :  bag(T)@i
5.  bs  =  (\{x\}  +  bag-drop(eq;bs;x))
6.  bag-no-repeats(T;bs)@i
7.  x  \mdownarrow{}\mmember{}  bs@i
8.  bs  =  (\{x\}  +  bag-drop(eq;bs;x))
\mvdash{}  bag-no-repeats(T;bag-drop(eq;bs;x))


By

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Latex:
(BLemma  `bag-drop-no-repeats`  THEN  Auto)

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