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Step * 1 1 of Lemma wellfounded-acyclic-rel


1. T : Type
2. R : T ⟶ T ⟶ ℙ
3. SWellFounded(x R y)@i
4. SWellFounded(x R+ y)
5. x : T@i
6. x R+ x@i
⊢ False
BY
{ (D 4 THEN InstHyp [⌜x⌝;⌜x⌝] (-3)⋅ THEN Auto) }

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Latex:

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Latex:

1.  T  :  Type
2.  R  :  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}
3.  SWellFounded(x  R  y)@i
4.  SWellFounded(x  R\msupplus{}  y)
5.  x  :  T@i
6.  x  R\msupplus{}  x@i
\mvdash{}  False


By

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Latex:
(D  4  THEN  InstHyp  [\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]  (-3)\mcdot{}  THEN  Auto)

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