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Step * 1 1 of Lemma geo-le_witness


1. e : BasicGeometry
2. {p:Point| O_X_p}  ⊆r Length
3. p : {p:Point| O_X_p} 
4. q : {p:Point| O_X_p} 
5. X_p_q
⊢ ∃q':{p:Point| O_X_p} . ((p = p ∈ Length) ∧ (q' = q ∈ Length) ∧ X_p_q')
BY
{ (D 0 With ⌜q⌝  THEN Auto) }

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  \{p:Point|  O\_X\_p\}    \msubseteq{}r  Length
3.  p  :  \{p:Point|  O\_X\_p\} 
4.  q  :  \{p:Point|  O\_X\_p\} 
5.  X\_p\_q
\mvdash{}  \mexists{}q':\{p:Point|  O\_X\_p\}  .  ((p  =  p)  \mwedge{}  (q'  =  q)  \mwedge{}  X\_p\_q')


By

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Latex:
(D  0  With  \mkleeneopen{}q\mkleeneclose{}    THEN  Auto)

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