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Step * 1 2 of Lemma hdf-until-halt-right


1. A : Type
2. B : Type
3. u : A
4. v : A List
5. ∀X:hdataflow(A;B). hdf-halted(hdf-until(X;hdf-halt())*(v)) = hdf-halted(X*(v))
6. X : hdataflow(A;B)@i
⊢ hdf-halted(fst(hdf-until(X;hdf-halt())(u))*(v)) = hdf-halted(fst(X(u))*(v))
BY
{ ((InstLemma `hdf-until-ap` [⌈A⌉;⌈B⌉;⌈Top⌉;⌈X⌉;⌈hdf-halt()⌉;⌈u⌉]⋅ THENA Auto)
   THEN HypSubst (-1) 0
   THEN Reduce 0
   THEN Auto) }

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Latex:



1.  A  :  Type
2.  B  :  Type
3.  u  :  A
4.  v  :  A  List
5.  \mforall{}X:hdataflow(A;B).  hdf-halted(hdf-until(X;hdf-halt())*(v))  =  hdf-halted(X*(v))
6.  X  :  hdataflow(A;B)@i
\mvdash{}  hdf-halted(fst(hdf-until(X;hdf-halt())(u))*(v))  =  hdf-halted(fst(X(u))*(v))


By

((InstLemma  `hdf-until-ap`  [\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}Top\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}hdf-halt()\mkleeneclose{};\mkleeneopen{}u\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  HypSubst  (-1)  0
  THEN  Reduce  0
  THEN  Auto)

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