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Step * of Lemma assert-lg-is-source

∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[i:ℕlg-size(g)].  uiff(↑lg-is-source(g;i);∀[j:ℕlg-size(g)]. (¬lg-edge(g;j;i)))
BY
{ (RepUR ``lg-is-source lg-edge`` 0
   THEN (UnivCD THENA Auto)
   THEN AutoSplit
   THEN GenConcl ⌜lg-in-edges(g;i) = L ∈ (ℕlg-size(g) List)⌝⋅
   THEN Auto) }

1
1. T : Type
2. g : LabeledGraph(T)
3. i : ℕlg-size(g)
4. i < lg-size(g)
5. L : ℕlg-size(g) List@i
6. lg-in-edges(g;i) = L ∈ (ℕlg-size(g) List)@i
7. ∀[j:ℕlg-size(g)]. (¬(j ∈ L))
⊢ L = [] ∈ (ℕlg-size(g) List)

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[g:LabeledGraph(T)].  \mforall{}[i:\mBbbN{}lg-size(g)].
    uiff(\muparrow{}lg-is-source(g;i);\mforall{}[j:\mBbbN{}lg-size(g)].  (\mneg{}lg-edge(g;j;i)))


By

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Latex:
(RepUR  ``lg-is-source  lg-edge``  0
  THEN  (UnivCD  THENA  Auto)
  THEN  AutoSplit
  THEN  GenConcl  \mkleeneopen{}lg-in-edges(g;i)  =  L\mkleeneclose{}\mcdot{}
  THEN  Auto)

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