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Step * 1 1 of Lemma eu-inner-pasch-ex


1. e : EuclideanPlane@i'
2. a : Point@i
3. b : Point@i
4. c : {c:Point| ¬Colinear(a;b;c)} @i
5. p : {p:Point| a-p-c} @i
6. q : {q:Point| b_q_c} @i
7. p-eu-inner-pasch(e;a;b;c;p;q)-b ∧ q-eu-inner-pasch(e;a;b;c;p;q)-a
⊢ p-eu-inner-pasch(e;a;b;c;p;q)-b
∧ q-eu-inner-pasch(e;a;b;c;p;q)-a
∧ (eu-inner-pasch(e;a;b;c;p;q) = eu-inner-pasch(e;a;b;c;p;q) ∈ Point)
BY
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Latex:

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Latex:

1.  e  :  EuclideanPlane@i'
2.  a  :  Point@i
3.  b  :  Point@i
4.  c  :  \{c:Point|  \mneg{}Colinear(a;b;c)\}  @i
5.  p  :  \{p:Point|  a-p-c\}  @i
6.  q  :  \{q:Point|  b\_q\_c\}  @i
7.  p-eu-inner-pasch(e;a;b;c;p;q)-b  \mwedge{}  q-eu-inner-pasch(e;a;b;c;p;q)-a
\mvdash{}  p-eu-inner-pasch(e;a;b;c;p;q)-b
\mwedge{}  q-eu-inner-pasch(e;a;b;c;p;q)-a
\mwedge{}  (eu-inner-pasch(e;a;b;c;p;q)  =  eu-inner-pasch(e;a;b;c;p;q))


By

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Latex:
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