Step
*
1
1
of Lemma
full-Pasch-lemma
1. e : EuclideanPlane
2. a : Point
3. x : Point
4. y : Point
5. d : Point
6. p : Point
7. d leftof xa
8. x-p-a
9. d # py
10. a leftof xy
11. y leftof ax
12. b : Point
13. Colinear(a;x;b)
14. B(ybd)
15. a leftof py
⊢ ∃p':Point. ((x-p'-y ∨ a-p'-y) ∧ Colinear(d;p;p'))
BY
{ (Assert b # y BY
((((Assert a # xy BY Unfold `geo-lsep` 0) THEN Auto) THEN InstLemma `geo-sep-or` [⌜e⌝;⌜a⌝;⌜x⌝;⌜b⌝]⋅ THEN Auto)
THEN D -1
)) }
1
.....aux.....
1. e : EuclideanPlane
2. a : Point
3. x : Point
4. y : Point
5. d : Point
6. p : Point
7. d leftof xa
8. x-p-a
9. d # py
10. a leftof xy
11. y leftof ax
12. b : Point
13. Colinear(a;x;b)
14. B(ybd)
15. a leftof py
16. a # xy
17. a # b
⊢ b # y
2
.....aux.....
1. e : EuclideanPlane
2. a : Point
3. x : Point
4. y : Point
5. d : Point
6. p : Point
7. d leftof xa
8. x-p-a
9. d # py
10. a leftof xy
11. y leftof ax
12. b : Point
13. Colinear(a;x;b)
14. B(ybd)
15. a leftof py
16. a # xy
17. x # b
⊢ b # y
3
1. e : EuclideanPlane
2. a : Point
3. x : Point
4. y : Point
5. d : Point
6. p : Point
7. d leftof xa
8. x-p-a
9. d # py
10. a leftof xy
11. y leftof ax
12. b : Point
13. Colinear(a;x;b)
14. B(ybd)
15. a leftof py
16. b # y
⊢ ∃p':Point. ((x-p'-y ∨ a-p'-y) ∧ Colinear(d;p;p'))
Latex:
Latex:
1. e : EuclideanPlane
2. a : Point
3. x : Point
4. y : Point
5. d : Point
6. p : Point
7. d leftof xa
8. x-p-a
9. d \# py
10. a leftof xy
11. y leftof ax
12. b : Point
13. Colinear(a;x;b)
14. B(ybd)
15. a leftof py
\mvdash{} \mexists{}p':Point. ((x-p'-y \mvee{} a-p'-y) \mwedge{} Colinear(d;p;p'))
By
Latex:
(Assert b \# y BY
((((Assert a \# xy BY Unfold `geo-lsep` 0) THEN Auto)
THEN InstLemma `geo-sep-or` [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{}]\mcdot{}
THEN Auto)
THEN D -1
))
Home
Index