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Step * 1 1 of Lemma rec-nat-induction

.....basecase..... 
1. P : ℕ ⟶ ℙ
2. Top ⊆r P[0]
3. f : ⋂n:ℕ. (P[n] ⇒ P[n + 1])@i
4. n : ℤ
⊢ fix(f) ∈ P[0]
BY
{ (SubsumeC ⌜Top⌝⋅ THEN Auto)⋅ }

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Latex:

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Latex:
.....basecase..... 
1.  P  :  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}
2.  Top  \msubseteq{}r  P[0]
3.  f  :  \mcap{}n:\mBbbN{}.  (P[n]  {}\mRightarrow{}  P[n  +  1])@i
4.  n  :  \mBbbZ{}
\mvdash{}  fix(f)  \mmember{}  P[0]


By

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Latex:
(SubsumeC  \mkleeneopen{}Top\mkleeneclose{}\mcdot{}  THEN  Auto)\mcdot{}

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