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Step * of Lemma Euclid-Prop28_2

∀e:EuclideanPlane. ∀a,b,c,d,x,y,p:Point.
  (((Colinear(x;a;b) ∧ Colinear(y;c;d)) ∧ (a leftof yx ∧ a-x-b) ∧ (c leftof xy ∧ c-y-d) ∧ p-x-y ∧ Ryxa ∧ Rxyc)
  ⇒ geo-parallel-points(e;a;b;c;d))
BY
{ (Auto THEN InstLemma  `adjacent-right-angles-supplementary` [⌜e⌝;⌜y⌝;⌜x⌝;⌜a⌝;⌜b⌝]⋅ THEN Auto) }

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. Ryxa
17. Rxyc
18. Ryxa ⇐ yxa ≅a yxb
19. yxa ≅a yxb
⊢ geo-parallel-points(e;a;b;c;d)

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Latex:

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Latex:
\mforall{}e:EuclideanPlane.  \mforall{}a,b,c,d,x,y,p:Point.
    (((Colinear(x;a;b)  \mwedge{}  Colinear(y;c;d))
    \mwedge{}  (a  leftof  yx  \mwedge{}  a-x-b)
    \mwedge{}  (c  leftof  xy  \mwedge{}  c-y-d)
    \mwedge{}  p-x-y
    \mwedge{}  Ryxa
    \mwedge{}  Rxyc)
    {}\mRightarrow{}  geo-parallel-points(e;a;b;c;d))


By

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Latex:
(Auto  THEN  InstLemma    `adjacent-right-angles-supplementary`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}  THEN  Auto)

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