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Step * 2 1 of Lemma lg-acyclic-well-founded


1. [T] : Type
2. ∀n:ℕ. ∀g:LabeledGraph(T).  (lg-size(g) < n ⇒ lg-acyclic(g) ⇒ SWellFounded(lg-edge(g;a;b)))
3. g : LabeledGraph(T)@i
4. lg-acyclic(g)@i
⊢ SWellFounded(lg-edge(g;a;b))
BY
{ (InstHyp [⌈lg-size(g) + 1⌉;⌈g⌉] 2⋅ THEN Auto THEN Auto')⋅ }

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Latex:

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Latex:

1.  [T]  :  Type
2.  \mforall{}n:\mBbbN{}.  \mforall{}g:LabeledGraph(T).    (lg-size(g)  <  n  {}\mRightarrow{}  lg-acyclic(g)  {}\mRightarrow{}  SWellFounded(lg-edge(g;a;b)))
3.  g  :  LabeledGraph(T)@i
4.  lg-acyclic(g)@i
\mvdash{}  SWellFounded(lg-edge(g;a;b))


By

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Latex:
(InstHyp  [\mkleeneopen{}lg-size(g)  +  1\mkleeneclose{};\mkleeneopen{}g\mkleeneclose{}]  2\mcdot{}  THEN  Auto  THEN  Auto')\mcdot{}

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