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Step * of Lemma l_sum-triangle-inequality

∀[T:Type]. ∀[L:T List]. ∀[f,g:T ⟶ ℤ].
  (|l_sum(map(λa.f[a];L)) - l_sum(map(λa.g[a];L))| ≤ l_sum(map(λa.|f[a] - g[a]|;L)))
BY
{ ((InstLemma `l_sum-triangle-inequality-general` [] THEN RepeatFor 2 (ParallelLast'))
   THEN (InstHyp [⌜0⌝;⌜0⌝] (-1)⋅ THENA Auto)
   THEN RepeatFor 2 (ParallelLast')
   THEN NthHypEq (-1)
   THEN EqCD
   THEN Auto
   THEN Subst' |0 - 0| ~ 0 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[f,g:T  {}\mrightarrow{}  \mBbbZ{}].
    (|l\_sum(map(\mlambda{}a.f[a];L))  -  l\_sum(map(\mlambda{}a.g[a];L))|  \mleq{}  l\_sum(map(\mlambda{}a.|f[a]  -  g[a]|;L)))


By

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Latex:
((InstLemma  `l\_sum-triangle-inequality-general`  []  THEN  RepeatFor  2  (ParallelLast'))
  THEN  (InstHyp  [\mkleeneopen{}0\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{}]  (-1)\mcdot{}  THENA  Auto)
  THEN  RepeatFor  2  (ParallelLast')
  THEN  NthHypEq  (-1)
  THEN  EqCD
  THEN  Auto
  THEN  Subst'  |0  -  0|  \msim{}  0  0
  THEN  Auto)

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