Step * 1 2 of Lemma Euclid-Prop26-2

.....assertion..... 
1. EuclideanPlane
2. Point
3. Point
4. Point
5. Point
6. Point
7. Point
8. bc
9. yz
10. abc ≅a xyz
11. bac ≅a yxz
12. ac ≅ xz
13. xy > ab
⊢ False
BY
(((D -1 THEN ExRepD) THEN (Assert x-w-y BY (D THEN Auto)))
   THEN (Assert xyz < xwz BY
               ((InstLemma  `Euclid-prop16` [⌜e⌝;⌜z⌝;⌜y⌝;⌜w⌝;⌜x⌝]⋅ THEN Auto)
                THEN InstLemma  `geo-out-preserves-lt-angle` [⌜e⌝;⌜w⌝;⌜y⌝;⌜z⌝;⌜x⌝;⌜z⌝;⌜z⌝;⌜w⌝;⌜x⌝]⋅
                THEN EAuto 1))
   THEN InstLemma  `lt-angle-not-cong2` [⌜e⌝;⌜x⌝;⌜y⌝;⌜z⌝;⌜x⌝;⌜w⌝;⌜z⌝]⋅
   THEN Auto) }

1
1. EuclideanPlane
2. Point
3. Point
4. Point
5. Point
6. Point
7. Point
8. bc
9. yz
10. abc ≅a xyz
11. bac ≅a yxz
12. ac ≅ xz
13. Point
14. x_w_y
15. xw ≅ ab
16. w ≠ y
17. x-w-y
18. xyz < xwz
19. ¬xyz ≅a xwz
⊢ False


Latex:


Latex:
.....assertion..... 
1.  e  :  EuclideanPlane
2.  a  :  Point
3.  b  :  Point
4.  c  :  Point
5.  x  :  Point
6.  y  :  Point
7.  z  :  Point
8.  a  \#  bc
9.  x  \#  yz
10.  abc  \mcong{}\msuba{}  xyz
11.  bac  \mcong{}\msuba{}  yxz
12.  ac  \mcong{}  xz
13.  xy  >  ab
\mvdash{}  False


By


Latex:
(((D  -1  THEN  ExRepD)  THEN  (Assert  x-w-y  BY  (D  0  THEN  Auto)))
  THEN  (Assert  xyz  <  xwz  BY
                          ((InstLemma    `Euclid-prop16`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THEN  Auto)
                            THEN  InstLemma    `geo-out-preserves-lt-angle`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}
                            THEN  EAuto  1))
  THEN  InstLemma    `lt-angle-not-cong2`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{}]\mcdot{}
  THEN  Auto)




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