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Step * of Lemma absval_div_decreases

∀[n:{2...}]. ∀[i:ℤ-o].  |i ÷ n| < |i|
BY
{ (Auto
   THEN (RWO "absval_div_nat<" 0 THENA Auto)
   THEN (InstLemma `div_rem_sum` [⌜|i|⌝;⌜n⌝]⋅ THENA Auto)
   THEN (InstLemma `rem_bounds_1` [⌜|i|⌝;⌜n⌝]⋅ THENA Auto)) }

1
1. n : {2...}
2. i : ℤ-o
3. |i| = (((|i| ÷ n) * n) + (|i| rem n)) ∈ ℤ
4. (0 ≤ (|i| rem n)) ∧ |i| rem n < n
⊢ |i| ÷ n < |i|

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Latex:

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Latex:
\mforall{}[n:\{2...\}].  \mforall{}[i:\mBbbZ{}\msupminus{}\msupzero{}].    |i  \mdiv{}  n|  <  |i|


By

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Latex:
(Auto
  THEN  (RWO  "absval\_div\_nat<"  0  THENA  Auto)
  THEN  (InstLemma  `div\_rem\_sum`  [\mkleeneopen{}|i|\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (InstLemma  `rem\_bounds\_1`  [\mkleeneopen{}|i|\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto))

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