---

Step * of Lemma real-vec-dist-dim1

∀[x,y:ℝ^1].  (d(x;y) = |(x 0) - y 0|)
BY
{ (Auto
   THEN RepUR ``real-vec-dist`` 0
   THEN RWO "real-vec-norm-dim1" 0
   THEN Auto
   THEN RepUR ``real-vec-sub`` 0
   THEN Auto) }

---

Latex:

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Latex:
\mforall{}[x,y:\mBbbR{}\^{}1].    (d(x;y)  =  |(x  0)  -  y  0|)


By

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Latex:
(Auto
  THEN  RepUR  ``real-vec-dist``  0
  THEN  RWO  "real-vec-norm-dim1"  0
  THEN  Auto
  THEN  RepUR  ``real-vec-sub``  0
  THEN  Auto)

---

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