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Step * of Lemma center-on-circle-overlap

∀e:EuclideanPlane. ∀a,b,c:Point.  (a ≠ b ⇒ |bc| ≤ |ab| + |ab| ⇒ Overlap(a;b;b;c))
BY
{ (Auto
   THEN D 0
   THEN D 0 With ⌜b⌝ 
   THEN Auto
   THEN InstLemma  `geo-SCS_wf` [⌜e⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜b⌝]⋅
   THEN Auto
   THEN D 0 With ⌜SCS(a;b;b;c)⌝ 
   THEN Auto) }

1
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. a ≠ b
6. |bc| ≤ |ab| + |ab|
7. SCS(a;b;b;c) ∈ {v:Point| bv ≅ bc ∧ (v_b_SCO(a;b;b;c) ∧ Colinear(a;b;v)) ∧ (b ≠ c ⇒ v ≠ SCO(a;b;b;c))} 
8. ab ≅ ab
9. bc ≥ bb
10. bc ≅ bSCS(a;b;b;c)
⊢ ab ≥ aSCS(a;b;b;c)

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Latex:

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Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c:Point.    (a  \mneq{}  b  {}\mRightarrow{}  |bc|  \mleq{}  |ab|  +  |ab|  {}\mRightarrow{}  Overlap(a;b;b;c))


By

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Latex:
(Auto
  THEN  D  0
  THEN  D  0  With  \mkleeneopen{}b\mkleeneclose{} 
  THEN  Auto
  THEN  InstLemma    `geo-SCS\_wf`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  D  0  With  \mkleeneopen{}SCS(a;b;b;c)\mkleeneclose{} 
  THEN  Auto)

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