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Step * 1 1 1 of Lemma empty-bag-iff-size


1. T : Type
2. bs : bag(T)
3. ∀x:T. (¬x ↓∈ bs)
⊢ #(bs) ≤ 0
BY
{ (SupposeNot
   THEN Assert ⌜0 < #(bs)⌝⋅
   THEN Auto
   THEN FLemma `bag-member-iff-size` [-1] ⋅
   THEN Auto
   THEN Assert ⌜False⌝⋅
   THEN Auto
   THEN ExRepD
   THEN Auto) }

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Latex:

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Latex:

1.  T  :  Type
2.  bs  :  bag(T)
3.  \mforall{}x:T.  (\mneg{}x  \mdownarrow{}\mmember{}  bs)
\mvdash{}  \#(bs)  \mleq{}  0


By

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Latex:
(SupposeNot
  THEN  Assert  \mkleeneopen{}0  <  \#(bs)\mkleeneclose{}\mcdot{}
  THEN  Auto
  THEN  FLemma  `bag-member-iff-size`  [-1]  \mcdot{}
  THEN  Auto
  THEN  Assert  \mkleeneopen{}False\mkleeneclose{}\mcdot{}
  THEN  Auto
  THEN  ExRepD
  THEN  Auto)

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