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Step * 1 3 of Lemma cong-angle-preserves-lsep_weak


1. g : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. x : Point
6. y : Point
7. z : Point
8. x # yz
9. abc ≅a xyz
10. Colinear(a;b;c)
11. ¬c # ab
12. b-c-a
⊢ False
BY
{ (((InstLemma `angle-cong-preserves-zero-angle` [⌜g⌝;⌜x⌝;⌜y⌝;⌜z⌝;⌜a⌝;⌜b⌝;⌜c⌝]⋅ THEN EAuto 1)
    THENA (InstLemma `geo-between-out` [⌜g⌝;⌜b⌝;⌜c⌝;⌜a⌝]⋅ THEN EAuto 1)
    )
   THEN FLemma `not-lsep-if-out` [-1]
   THEN Auto) }

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Latex:

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Latex:

1.  g  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  x  :  Point
6.  y  :  Point
7.  z  :  Point
8.  x  \#  yz
9.  abc  \mcong{}\msuba{}  xyz
10.  Colinear(a;b;c)
11.  \mneg{}c  \#  ab
12.  b-c-a
\mvdash{}  False


By

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Latex:
(((InstLemma  `angle-cong-preserves-zero-angle`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  EAuto  1)
    THENA  (InstLemma  `geo-between-out`  [\mkleeneopen{}g\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}  THEN  EAuto  1)
    )
  THEN  FLemma  `not-lsep-if-out`  [-1]
  THEN  Auto)

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