Step
*
1
of Lemma
geo-between-out-implies-out3
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a # t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
⊢ {(out(a ct) ∧ out(a bt)) ∧ out(a c't) ∧ out(a b't)}
BY
{ ((RepeatFor 3 (D 0) THEN Auto) THEN (D 0 THENA Auto)) }
1
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a # t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
15. a # t
16. (¬B(act)) ∧ (¬B(atc))
⊢ False
2
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a # t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
15. a # t
16. (¬B(abt)) ∧ (¬B(atb))
⊢ False
3
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a # t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
15. a # t
16. (¬B(ac't)) ∧ (¬B(atc'))
⊢ False
4
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a # t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
15. a # t
16. (¬B(ab't)) ∧ (¬B(atb'))
⊢ False
Latex:
Latex:
1. e : EuclideanPlane
2. a : Point
3. b : Point
4. b' : Point
5. c : Point
6. c' : Point
7. t : Point
8. out(a bb')
9. out(a cc')
10. a-b-c
11. B(b'tc')
12. a \# t
13. Colinear(a;c';t)
14. Colinear(a;b';t)
\mvdash{} \{(out(a ct) \mwedge{} out(a bt)) \mwedge{} out(a c't) \mwedge{} out(a b't)\}
By
Latex:
((RepeatFor 3 (D 0) THEN Auto) THEN (D 0 THENA Auto))
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