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Step * 1 of Lemma rn-metric-complete


1. n : ℕ
2. n = 0 ∈ ℤ
⊢ ∃c1,c2:{s:ℝ| r0 < s} . (c1*rn-prod-metric(0) ≤ rn-metric(0) ∧ c2*rn-metric(0) ≤ rn-prod-metric(0))
BY
{ (InstConcl [⌜r1⌝;⌜r1⌝]⋅
   THEN Auto
   THEN (D 0 THEN Auto)
   THEN RepUR ``scale-metric rn-prod-metric rn-metric prod-metric`` 0
   THEN RepUR ``mdist rmetric`` 0
   THEN RWO "rsum-empty" 0
   THEN Auto
   THEN nRNorm 0
   THEN Auto) }

1
1. n : ℕ
2. n = 0 ∈ ℤ
3. r1*rn-prod-metric(0) ≤ rn-metric(0)
4. x : ℝ^0
5. y : ℝ^0
⊢ d(x;y) ≤ r0

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  n  =  0
\mvdash{}  \mexists{}c1,c2:\{s:\mBbbR{}|  r0  <  s\}  .  (c1*rn-prod-metric(0)  \mleq{}  rn-metric(0)  \mwedge{}  c2*rn-metric(0)  \mleq{}  rn-prod-metric(0))


By

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Latex:
(InstConcl  [\mkleeneopen{}r1\mkleeneclose{};\mkleeneopen{}r1\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  (D  0  THEN  Auto)
  THEN  RepUR  ``scale-metric  rn-prod-metric  rn-metric  prod-metric``  0
  THEN  RepUR  ``mdist  rmetric``  0
  THEN  RWO  "rsum-empty"  0
  THEN  Auto
  THEN  nRNorm  0
  THEN  Auto)

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