Step * 1 1 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. ab > xy
⊢ False
BY
((((D -1 THEN ExRepD) THEN (Assert a-w-b BY (D THEN Auto)))
    THEN InstLemma  `colinear-lsep` [⌜e⌝;⌜b⌝;⌜a⌝;⌜c⌝;⌜w⌝]⋅
    THEN Auto)
   THEN (Assert abc < awc BY
               ((InstLemma  `Euclid-prop16` [⌜e⌝;⌜c⌝;⌜b⌝;⌜w⌝;⌜a⌝]⋅ THEN Auto)
                THEN InstLemma  `geo-out-preserves-lt-angle` [⌜e⌝;⌜w⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜c⌝;⌜c⌝;⌜w⌝;⌜a⌝]⋅
                THEN EAuto 1))
   THEN InstLemma  `lt-angle-not-cong2` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜a⌝;⌜w⌝;⌜c⌝]⋅
   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. a_w_b
15. aw ≅ xy
16. w ≠ b
17. a-w-b
18. ac
19. abc < awc
20. ¬abc ≅a awc
⊢ 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.  ab  >  xy
\mvdash{}  False


By


Latex:
((((D  -1  THEN  ExRepD)  THEN  (Assert  a-w-b  BY  (D  0  THEN  Auto)))
    THEN  InstLemma    `colinear-lsep`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{}]\mcdot{}
    THEN  Auto)
  THEN  (Assert  abc  <  awc  BY
                          ((InstLemma    `Euclid-prop16`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}  THEN  Auto)
                            THEN  InstLemma    `geo-out-preserves-lt-angle`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}
                            THEN  EAuto  1))
  THEN  InstLemma    `lt-angle-not-cong2`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
  THEN  Auto)




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