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Step * of Lemma geo-congruent-preserves-strict-between

∀e:BasicGeometry. ∀a,b,c,a',b',c':Point.  (a-b-c ⇒ ab ≅ a'b' ⇒ ac ≅ a'c' ⇒ bc ≅ b'c' ⇒ a'-b'-c')
BY
{ (Auto THEN ((InstLemma `geo-congruent-between-exists` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜a'⌝;⌜c'⌝]⋅ THENM ExRepD) THENA Auto)) }

1
1. e : BasicGeometry
2. a : Point
3. b : Point
4. c : Point
5. a' : Point
6. b' : Point
7. c' : Point
8. a-b-c
9. ab ≅ a'b'
10. ac ≅ a'c'
11. bc ≅ b'c'
12. b1 : Point
13. a'_b1_c'
14. ab ≅ a'b1
15. bc ≅ b1c'
⊢ a'-b'-c'

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Latex:

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Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c,a',b',c':Point.    (a-b-c  {}\mRightarrow{}  ab  \mcong{}  a'b'  {}\mRightarrow{}  ac  \mcong{}  a'c'  {}\mRightarrow{}  bc  \mcong{}  b'c'  {}\mRightarrow{}  a'-b'-c')


By

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Latex:
(Auto
  THEN  ((InstLemma  `geo-congruent-between-exists`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a'\mkleeneclose{};\mkleeneopen{}c'\mkleeneclose{}]\mcdot{}  THENM  ExRepD)
              THENA  Auto
              )
  )

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