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Step * 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
⊢ ∃x:Point. (p-x-b ∧ q-x-a ∧ (x = eu-inner-pasch(e;a;b;c;p;q) ∈ Point))
BY
{ (InstConcl [⌜eu-inner-pasch(e;a;b;c;p;q)⌝]⋅ THENA Auto)
THEN (InstLemma `eu-inner-pasch-property` [⌜e⌝;⌜a⌝;⌜b⌝;⌜c⌝;⌜p⌝;⌜q⌝]⋅ THENA Auto) }

1
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)

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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
\mvdash{}  \mexists{}x:Point.  (p-x-b  \mwedge{}  q-x-a  \mwedge{}  (x  =  eu-inner-pasch(e;a;b;c;p;q)))


By

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Latex:
(InstConcl  [\mkleeneopen{}eu-inner-pasch(e;a;b;c;p;q)\mkleeneclose{}]\mcdot{}  THENA  Auto)
THEN  (InstLemma  `eu-inner-pasch-property`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}p\mkleeneclose{};\mkleeneopen{}q\mkleeneclose{}]\mcdot{}  THENA  Auto)

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