Step
*
1
of Lemma
lsep-inner-pasch-strict
1. e : OrientedPlane
2. a : Point
3. b : Point
4. c : {c:Point| c # ab}
5. p : {p:Point| a-p-c}
6. q : {q:Point| b-q-c}
7. ∃x:{Point| (b_x_p ∧ a_x_q)}
8. c # ab
9. a-p-c
10. b-q-c
11. c # aq
12. b # aq
13. c # pb
14. a # pb
⊢ ∃x:{Point| (b-x-p ∧ a-x-q)}
BY
{ ExRepD }
1
1. e : OrientedPlane
2. a : Point
3. b : Point
4. c : {c:Point| c # ab}
5. p : {p:Point| a-p-c}
6. q : {q:Point| b-q-c}
7. x : Point
8. b_x_p
9. a_x_q
10. c # ab
11. a-p-c
12. b-q-c
13. c # aq
14. b # aq
15. c # pb
16. a # pb
⊢ ∃x:{Point| (b-x-p ∧ a-x-q)}
Latex:
Latex:
1. e : OrientedPlane
2. a : Point
3. b : Point
4. c : \{c:Point| c \# ab\}
5. p : \{p:Point| a-p-c\}
6. q : \{q:Point| b-q-c\}
7. \mexists{}x:\{Point| (b\_x\_p \mwedge{} a\_x\_q)\}
8. c \# ab
9. a-p-c
10. b-q-c
11. c \# aq
12. b \# aq
13. c \# pb
14. a \# pb
\mvdash{} \mexists{}x:\{Point| (b-x-p \mwedge{} a-x-q)\}
By
Latex:
ExRepD
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