Step * of Lemma bag-parts'_wf2

[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[bs:bag(T)].  (bag-parts'(eq;bs;x) ∈ bag({L:bag(T) List+| ¬x ↓∈ hd(L)} )) suppos\000Cing valueall-type(T)
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1
1. Type
2. valueall-type(T)
3. eq EqDecider(T)
4. T
5. bs bag(T)
⊢ bag-parts'(eq;bs;x) ∈ bag({L:bag(T) List+| ¬x ↓∈ hd(L)} )


Latex:


Latex:
\mforall{}[T:Type]
    \mforall{}[eq:EqDecider(T)].  \mforall{}[x:T].  \mforall{}[bs:bag(T)].
        (bag-parts'(eq;bs;x)  \mmember{}  bag(\{L:bag(T)  List\msupplus{}|  \mneg{}x  \mdownarrow{}\mmember{}  hd(L)\}  )) 
    supposing  valueall-type(T)


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