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Step * 2 of Lemma Euclid-Prop28_1


1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. x : Point
7. y : Point
8. p : Point
9. Colinear(x;a;b)
10. Colinear(y;c;d)
11. a leftof yx
12. a-x-b
13. c leftof xy
14. c-y-d
15. p-x-y
16. bxp ≅a cyx
17. bxp ≅a axy
⊢ geo-parallel-points(e;a;b;c;d)
BY
{ ((InstLemma `Euclid-Prop27` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜d⌝;⌜x⌝;⌜y⌝]⋅ THEN Auto)
   THEN InstLemma `geo-cong-angle-transitivity` [⌜e⌝;⌜a⌝;⌜x⌝;⌜y⌝;⌜b⌝;⌜x⌝;⌜p⌝;⌜c⌝;⌜y⌝;⌜x⌝]⋅
   THEN EAuto 1) }

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Latex:

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Latex:

1.  e  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  d  :  Point
6.  x  :  Point
7.  y  :  Point
8.  p  :  Point
9.  Colinear(x;a;b)
10.  Colinear(y;c;d)
11.  a  leftof  yx
12.  a-x-b
13.  c  leftof  xy
14.  c-y-d
15.  p-x-y
16.  bxp  \mcong{}\msuba{}  cyx
17.  bxp  \mcong{}\msuba{}  axy
\mvdash{}  geo-parallel-points(e;a;b;c;d)


By

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Latex:
((InstLemma  `Euclid-Prop27`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  InstLemma  `geo-cong-angle-transitivity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}
  THEN  EAuto  1)

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