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Step * 2 1 of Lemma rn-metric-complete


1. n : ℕ
2. ¬(n = 0 ∈ ℤ)
⊢ (r1/r(n))*rn-prod-metric(n) ≤ rn-metric(n)
BY
{ ((InstLemma `rn-prod-metric-le-max-metric` [⌜n⌝]⋅ THENA Auto)
   THEN (InstLemma `max-metric-leq-rn-metric` [⌜n⌝]⋅ THENA Auto)
   ) }

1
1. n : ℕ
2. ¬(n = 0 ∈ ℤ)
3. rn-prod-metric(n) ≤ r(n)*max-metric(n)
4. max-metric(n) ≤ rn-metric(n)
⊢ (r1/r(n))*rn-prod-metric(n) ≤ rn-metric(n)

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  \mneg{}(n  =  0)
\mvdash{}  (r1/r(n))*rn-prod-metric(n)  \mleq{}  rn-metric(n)


By

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Latex:
((InstLemma  `rn-prod-metric-le-max-metric`  [\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (InstLemma  `max-metric-leq-rn-metric`  [\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto)
  )

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