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Step * 1 2 1 1 1 of Lemma reducible-nat


1. n : ℤ@i
2. 2 ≤ n
3. b : ℤ-o@i
4. c : ℤ-o@i
5. ¬(b ~ 1)@i
6. ¬(c ~ 1)@i
7. n = (b * c) ∈ ℤ@i
8. ¬(2 ≤ b)
9. b ≤ (-2)
10. 2 ≤ (-c)
⊢ -b < n
BY
{ (SupposeNot
   THEN (InstLemma `mul_preserves_le` [⌜n⌝;⌜-b⌝;⌜-c⌝]⋅ THEN Auto)
   THEN InstLemma `mul_preserves_le` [⌜2⌝;⌜-c⌝;⌜n⌝]⋅
   THEN Auto')⋅ }

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Latex:

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Latex:

1.  n  :  \mBbbZ{}@i
2.  2  \mleq{}  n
3.  b  :  \mBbbZ{}\msupminus{}\msupzero{}@i
4.  c  :  \mBbbZ{}\msupminus{}\msupzero{}@i
5.  \mneg{}(b  \msim{}  1)@i
6.  \mneg{}(c  \msim{}  1)@i
7.  n  =  (b  *  c)@i
8.  \mneg{}(2  \mleq{}  b)
9.  b  \mleq{}  (-2)
10.  2  \mleq{}  (-c)
\mvdash{}  -b  <  n


By

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Latex:
(SupposeNot
  THEN  (InstLemma  `mul\_preserves\_le`  [\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}-b\mkleeneclose{};\mkleeneopen{}-c\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  InstLemma  `mul\_preserves\_le`  [\mkleeneopen{}2\mkleeneclose{};\mkleeneopen{}-c\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}
  THEN  Auto')\mcdot{}

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