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Step * 1 1 1 1 of Lemma geo-between-middle


1. e : BasicGeometry
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. a ≠ d
7. a_b_d
8. a_c_d
9. x : Point
10. d_a_x
11. ax ≅ da
12. x ≠ a
13. ¬b_c_d
14. ¬c_b_d
15. x_b_c
⊢ False
BY
{ (InstLemma `geo-between-exchange4` [⌜e⌝;⌜d⌝;⌜c⌝;⌜a⌝;⌜x⌝]⋅ THENA Auto)
THEN (InstLemma `geo-between-exchange3` [⌜e⌝;⌜x⌝;⌜b⌝;⌜c⌝;⌜d⌝]⋅ THENA Auto)
THEN Contradiction
⋅ }

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  d  :  Point
6.  a  \mneq{}  d
7.  a\_b\_d
8.  a\_c\_d
9.  x  :  Point
10.  d\_a\_x
11.  ax  \00D0  da
12.  x  \mneq{}  a
13.  \mneg{}b\_c\_d
14.  \mneg{}c\_b\_d
15.  x\_b\_c
\mvdash{}  False


By

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Latex:
(InstLemma  `geo-between-exchange4`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THENA  Auto)
THEN  (InstLemma  `geo-between-exchange3`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}  THENA  Auto)
THEN  Contradiction
\mcdot{}

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