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Step * of Lemma continuous-monotone-product

∀[F,G:Type ⟶ Type].
  (ContinuousMonotone(T.F[T] × G[T])) supposing (ContinuousMonotone(T.G[T]) and ContinuousMonotone(T.F[T]))
BY
{ (Unfold `so_apply` 0
   THEN Auto
   THEN RepeatFor 4 ((D 0 THEN Auto))
   THEN DoSubsume
   THEN Auto
   THEN BackThruSomeHyp'
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[F,G:Type  {}\mrightarrow{}  Type].
    (ContinuousMonotone(T.F[T]  \mtimes{}  G[T]))  supposing 
          (ContinuousMonotone(T.G[T])  and 
          ContinuousMonotone(T.F[T]))


By

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Latex:
(Unfold  `so\_apply`  0
  THEN  Auto
  THEN  RepeatFor  4  ((D  0  THEN  Auto))
  THEN  DoSubsume
  THEN  Auto
  THEN  BackThruSomeHyp'
  THEN  Auto)

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