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Step * of Lemma fix_wf_corec_parameter3

∀[F,A:Type ⟶ Type].
  ∀[G:Top ⟶ Top ⟶ Top ⋂ ⋂T:{T:Type| corec(T.F[T]) ⊆r T} . ((A[T] ⟶ T) ⟶ A[F[T]] ⟶ F[T])]. ∀[a:A[corec(T.F[T])]].
    (fix(G) a ∈ corec(T.F[T])) 
  supposing Continuous+(T.A[T])
BY
{ TACTIC:(Auto
          THEN InstLemma fix_wf_corec2' [⌜F⌝;⌜λ2T.A[T] ⟶ T⌝;⌜G⌝]⋅
          THEN Auto
          THEN Try ((ProveContinuous THEN Auto))
          THEN Isect2CD
          THEN Isect2HD' 4
          THEN Auto) }

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Latex:

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Latex:
\mforall{}[F,A:Type  {}\mrightarrow{}  Type].
    \mforall{}[G:Top  {}\mrightarrow{}  Top  {}\mrightarrow{}  Top  \mcap{}  \mcap{}T:\{T:Type|  corec(T.F[T])  \msubseteq{}r  T\}  .  ((A[T]  {}\mrightarrow{}  T)  {}\mrightarrow{}  A[F[T]]  {}\mrightarrow{}  F[T])].
    \mforall{}[a:A[corec(T.F[T])]].
        (fix(G)  a  \mmember{}  corec(T.F[T])) 
    supposing  Continuous+(T.A[T])


By

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Latex:
TACTIC:(Auto
                THEN  InstLemma  fix\_wf\_corec2'  [\mkleeneopen{}F\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}T.A[T]  {}\mrightarrow{}  T\mkleeneclose{};\mkleeneopen{}G\mkleeneclose{}]\mcdot{}
                THEN  Auto
                THEN  Try  ((ProveContinuous  THEN  Auto))
                THEN  Isect2CD
                THEN  Isect2HD'  4
                THEN  Auto)

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