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Step * of Lemma no-descending-chain-implies-wellfounded

∀[T:Type]. ∀[<:T ⟶ T ⟶ ℙ].
  ((∀x,y,z:T.  ((x < y) ⇒ (y < z) ⇒ (x < z)))
  ⇒ (∀x,y:T.  Dec(x < y))
  ⇒ no-descending-chain(T;<)
  ⇒ WellFnd{i}(T;x,y.x < y))
BY
{ (Auto
   THEN InstLemma `descending-chain-barred-implies-wellfounded`
    [⌜T⌝;⌜<⌝;⌜λx,y. (¬(x < y))⌝]⋅
   THEN Reduce 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[<:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    ((\mforall{}x,y,z:T.    ((x  <  y)  {}\mRightarrow{}  (y  <  z)  {}\mRightarrow{}  (x  <  z)))
    {}\mRightarrow{}  (\mforall{}x,y:T.    Dec(x  <  y))
    {}\mRightarrow{}  no-descending-chain(T;<)
    {}\mRightarrow{}  WellFnd\{i\}(T;x,y.x  <  y))


By

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Latex:
(Auto
  THEN  InstLemma  `descending-chain-barred-implies-wellfounded`
    [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}<\mkleeneclose{};\mkleeneopen{}\mlambda{}x,y.  (\mneg{}(x  <  y))\mkleeneclose{}]\mcdot{}
  THEN  Reduce  0
  THEN  Auto)

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