---

Step * of Lemma transitive-closure-contains

∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ].  R => TC(R)
BY
{ (Auto
   THEN D 0
   THEN Auto
   THEN RenameVar `r' (-1)
   THEN UseWitness ⌜[<x, y, r>]⌝ ⋅
   THEN RepUR ``transitive-closure`` 0
   THEN MemTypeCD
   THEN Auto
   THEN RepUR ``rel_path`` 0
   THEN Auto') }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[R:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].    R  =>  TC(R)


By

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Latex:
(Auto
  THEN  D  0
  THEN  Auto
  THEN  RenameVar  `r'  (-1)
  THEN  UseWitness  \mkleeneopen{}[<x,  y,  r>]\mkleeneclose{}  \mcdot{}
  THEN  RepUR  ``transitive-closure``  0
  THEN  MemTypeCD
  THEN  Auto
  THEN  RepUR  ``rel\_path``  0
  THEN  Auto')

---

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