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Step * 1 1 of Lemma prime-factors2

.....assertion..... 
1. n : {2...}
2. ∀n1:{2..n-}. (∃factors:{m:{2...}| prime(m)}  List [(n1 = Π(factors)  ∈ ℤ)])
⊢ Dec(∃n1:ℤ [(n1 < n ∧ (2 ≤ n1) ∧ (n1 | n))])
BY
{ TACTIC:Auto }

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Latex:

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Latex:
.....assertion..... 
1.  n  :  \{2...\}
2.  \mforall{}n1:\{2..n\msupminus{}\}.  (\mexists{}factors:\{m:\{2...\}|  prime(m)\}    List  [(n1  =  \mPi{}(factors)  )])
\mvdash{}  Dec(\mexists{}n1:\mBbbZ{}  [(n1  <  n  \mwedge{}  (2  \mleq{}  n1)  \mwedge{}  (n1  |  n))])


By

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Latex:
TACTIC:Auto

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