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Step * 1 1 of Lemma sequential-composition-inputs_wf


1. Info : Type
2. f : Name ─→ Type
3. X : EClass(Interface)
4. es : EO+(Info)
5. e : E
6. hdr : Name
7. single-valued-on-header{i:l}(Info;X;hdr)
8. ∀x:bag(Interface). (↑(#([x∈x|name_eq(msg-header(x.msg);hdr) ∧b x.dst = loc(e)]) =z 1) ∈ Type)
9. xs : bag(Interface)@i
10. #([x∈xs|name_eq(msg-header(x.msg);hdr) ∧b x.dst = loc(e)]) = 1 ∈ ℤ
⊢ single-valued-bag([x∈xs|name_eq(msg-header(x.msg);hdr) ∧b x.dst = loc(e)];Interface)
BY
{ (BLemma `single-valued-bag-if-le1` THEN Auto) }

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Latex:

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Latex:

1.  Info  :  Type
2.  f  :  Name  {}\mrightarrow{}  Type
3.  X  :  EClass(Interface)
4.  es  :  EO+(Info)
5.  e  :  E
6.  hdr  :  Name
7.  single-valued-on-header\{i:l\}(Info;X;hdr)
8.  \mforall{}x:bag(Interface).  (\muparrow{}(\#([x\mmember{}x|name\_eq(msg-header(x.msg);hdr)  \mwedge{}\msubb{}  x.dst  =  loc(e)])  =\msubz{}  1)  \mmember{}  Type)
9.  xs  :  bag(Interface)@i
10.  \#([x\mmember{}xs|name\_eq(msg-header(x.msg);hdr)  \mwedge{}\msubb{}  x.dst  =  loc(e)])  =  1
\mvdash{}  single-valued-bag([x\mmember{}xs|name\_eq(msg-header(x.msg);hdr)  \mwedge{}\msubb{}  x.dst  =  loc(e)];Interface)


By

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Latex:
(BLemma  `single-valued-bag-if-le1`  THEN  Auto)

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