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Step * of Lemma one_or_both-induction

∀[A,B:Type]. ∀[P:one_or_both(A;B) ⟶ ℙ].
  ((∀bval:A × B. P[oobboth(bval)])
  ⇒ (∀lval:A. P[oobleft(lval)])
  ⇒ (∀rval:B. P[oobright(rval)])
  ⇒ {∀x:one_or_both(A;B). P[x]})
BY
{ (Auto
   THEN D 0
   THEN Auto
   THEN RepeatFor 2 (D -1)
   THEN Try ((Folds ``oobleft oobright`` 0⋅ THEN Complete (Auto)))
   THEN Fold `oobboth` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A,B:Type].  \mforall{}[P:one\_or\_both(A;B)  {}\mrightarrow{}  \mBbbP{}].
    ((\mforall{}bval:A  \mtimes{}  B.  P[oobboth(bval)])
    {}\mRightarrow{}  (\mforall{}lval:A.  P[oobleft(lval)])
    {}\mRightarrow{}  (\mforall{}rval:B.  P[oobright(rval)])
    {}\mRightarrow{}  \{\mforall{}x:one\_or\_both(A;B).  P[x]\})


By

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Latex:
(Auto
  THEN  D  0
  THEN  Auto
  THEN  RepeatFor  2  (D  -1)
  THEN  Try  ((Folds  ``oobleft  oobright``  0\mcdot{}  THEN  Complete  (Auto)))
  THEN  Fold  `oobboth`  0
  THEN  Auto)

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