Step
*
1
1
1
1
of Lemma
eu-cong3-to-conga
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. E : Point
7. f : Point
8. a' : Point
9. c' : Point
10. d' : Point
11. f' : Point
12. out(b a'a)
13. out(b c'c)
14. out(E d'd)
15. out(E f'f)
16. a'b=d'E ∧ bc'=Ef' ∧ c'a'=f'd'
17. ¬(a = b ∈ Point)
18. ¬(c = b ∈ Point)
19. ¬(d = E ∈ Point)
20. ¬(f = E ∈ Point)
21. a0 : Point
22. b_a_a0 ∧ aa0=Ed
23. c0 : Point
24. b_c_c0 ∧ cc0=Ef
25. d0 : Point
26. E_d_d0 ∧ dd0=ba
27. f0 : Point
28. E_f_f0 ∧ ff0=bc
⊢ b_a_a0 ∧ b_c_c0 ∧ E_d_d0 ∧ E_f_f0 ∧ ba0=Ed0 ∧ bc0=Ef0 ∧ a0c0=d0f0
BY
{ ((Assert out(b aa') BY
InstLemma `eu-out-refl` [⌜e⌝;⌜b⌝;⌜a'⌝;⌜a⌝]⋅
THEN Auto)
THEN (Assert out(E dd') BY
InstLemma `eu-out-refl` [⌜e⌝;⌜E⌝;⌜d'⌝;⌜d⌝]⋅
THEN Auto)
THEN (InstLemma `eu-cong3-to-conga-aux` [⌜e⌝;⌜b⌝;⌜a⌝;⌜a'⌝;⌜a0⌝;⌜E⌝;⌜d⌝;⌜d'⌝;⌜d0⌝]⋅ THENA Auto)) }
1
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. E : Point
7. f : Point
8. a' : Point
9. c' : Point
10. d' : Point
11. f' : Point
12. out(b a'a)
13. out(b c'c)
14. out(E d'd)
15. out(E f'f)
16. a'b=d'E ∧ bc'=Ef' ∧ c'a'=f'd'
17. ¬(a = b ∈ Point)
18. ¬(c = b ∈ Point)
19. ¬(d = E ∈ Point)
20. ¬(f = E ∈ Point)
21. a0 : Point
22. b_a_a0 ∧ aa0=Ed
23. c0 : Point
24. b_c_c0 ∧ cc0=Ef
25. d0 : Point
26. E_d_d0 ∧ dd0=ba
27. f0 : Point
28. E_f_f0 ∧ ff0=bc
29. out(b aa')
30. out(E dd')
31. ba0=Ed0 ∧ a'a0=d'd0
⊢ b_a_a0 ∧ b_c_c0 ∧ E_d_d0 ∧ E_f_f0 ∧ ba0=Ed0 ∧ bc0=Ef0 ∧ a0c0=d0f0
Latex:
Latex:
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. c : Point
5. d : Point
6. E : Point
7. f : Point
8. a' : Point
9. c' : Point
10. d' : Point
11. f' : Point
12. out(b a'a)
13. out(b c'c)
14. out(E d'd)
15. out(E f'f)
16. a'b=d'E \mwedge{} bc'=Ef' \mwedge{} c'a'=f'd'
17. \mneg{}(a = b)
18. \mneg{}(c = b)
19. \mneg{}(d = E)
20. \mneg{}(f = E)
21. a0 : Point
22. b\_a\_a0 \mwedge{} aa0=Ed
23. c0 : Point
24. b\_c\_c0 \mwedge{} cc0=Ef
25. d0 : Point
26. E\_d\_d0 \mwedge{} dd0=ba
27. f0 : Point
28. E\_f\_f0 \mwedge{} ff0=bc
\mvdash{} b\_a\_a0 \mwedge{} b\_c\_c0 \mwedge{} E\_d\_d0 \mwedge{} E\_f\_f0 \mwedge{} ba0=Ed0 \mwedge{} bc0=Ef0 \mwedge{} a0c0=d0f0
By
Latex:
((Assert out(b aa') BY
InstLemma `eu-out-refl` [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a'\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{}]\mcdot{}
THEN Auto)
THEN (Assert out(E dd') BY
InstLemma `eu-out-refl` [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}E\mkleeneclose{};\mkleeneopen{}d'\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{}]\mcdot{}
THEN Auto)
THEN (InstLemma `eu-cong3-to-conga-aux` [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}a'\mkleeneclose{};\mkleeneopen{}a0\mkleeneclose{};\mkleeneopen{}E\mkleeneclose{};\mkleeneopen{}d\mkleeneclose{};\mkleeneopen{}d'\mkleeneclose{};\mkleeneopen{}d0\mkleeneclose{}]\mcdot{} THENA Auto))
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