Step * 1 of Lemma Euclid-Prop28_2


1. EuclideanPlane
2. Point
3. Point
4. Point
5. Point
6. Point
7. Point
8. Point
9. Colinear(x;a;b)
10. Colinear(y;c;d)
11. leftof yx
12. a-x-b
13. 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)
BY
((InstLemma  `Euclid-Prop27` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜d⌝;⌜x⌝;⌜y⌝]⋅ THEN Auto)
   THEN (InstLemma  `geo-right-angles-congruent` [⌜e⌝;⌜y⌝;⌜x⌝;⌜a⌝;⌜x⌝;⌜y⌝;⌜c⌝]⋅ THEN Auto)
   THEN FLemma  `geo-cong-angle-symmetry` [-1]
   THEN Auto) }


Latex:


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.  Ryxa
17.  Rxyc
18.  Ryxa  \mLeftarrow{}{}  yxa  \mcong{}\msuba{}  yxb
19.  yxa  \mcong{}\msuba{}  yxb
\mvdash{}  geo-parallel-points(e;a;b;c;d)


By


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-right-angles-congruent`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}  THEN  Auto)
  THEN  FLemma    `geo-cong-angle-symmetry`  [-1]
  THEN  Auto)




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