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Step * 2 of Lemma bag-subtype2


1. A : Type
2. P : A ⟶ ℙ
3. b : bag({x:A| P[x]} )
4. x : {x:A| P[x]} 
5. x ↓∈ b
⊢ x ↓∈ b
BY
{ (InstLemma `bag-member-subtype` [⌜{x:A| P[x]} ⌝;⌜A⌝;⌜b⌝;⌜x⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  A  :  Type
2.  P  :  A  {}\mrightarrow{}  \mBbbP{}
3.  b  :  bag(\{x:A|  P[x]\}  )
4.  x  :  \{x:A|  P[x]\} 
5.  x  \mdownarrow{}\mmember{}  b
\mvdash{}  x  \mdownarrow{}\mmember{}  b


By

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Latex:
(InstLemma  `bag-member-subtype`  [\mkleeneopen{}\{x:A|  P[x]\}  \mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THEN  Auto)

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