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Step * of Lemma fix_wf_corec-family-partial-nat

∀[P:Type]. ∀[H:(P ⟶ Type) ⟶ P ⟶ Type].
  ∀[f:⋂T:P ⟶ Type. ((i:P ⟶ (T i) ⟶ partial(ℕ)) ⟶ i:P ⟶ (H[T] i) ⟶ partial(ℕ))]
    (fix(f) ∈ i:P ⟶ (corec-family(H) i) ⟶ partial(ℕ)) 
  supposing family-monotone{i:l}(P;H) ∧ type-family-continuous{i:l}(P;H)
BY
{ Auto }

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Latex:

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Latex:
\mforall{}[P:Type].  \mforall{}[H:(P  {}\mrightarrow{}  Type)  {}\mrightarrow{}  P  {}\mrightarrow{}  Type].
    \mforall{}[f:\mcap{}T:P  {}\mrightarrow{}  Type.  ((i:P  {}\mrightarrow{}  (T  i)  {}\mrightarrow{}  partial(\mBbbN{}))  {}\mrightarrow{}  i:P  {}\mrightarrow{}  (H[T]  i)  {}\mrightarrow{}  partial(\mBbbN{}))]
        (fix(f)  \mmember{}  i:P  {}\mrightarrow{}  (corec-family(H)  i)  {}\mrightarrow{}  partial(\mBbbN{})) 
    supposing  family-monotone\{i:l\}(P;H)  \mwedge{}  type-family-continuous\{i:l\}(P;H)


By

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Latex:
Auto

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