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Step * 1 1 of Lemma geo-length-equality


1. e : BasicGeometry
2. p' : {p:Point| O_X_p} 
3. v : Point
4. [%2] : O_X_v ∧ Xv ≅ Xp'
5. extend OX by Xp' = v ∈ {x:Point| O_X_x ∧ Xx ≅ Xp'} 
⊢ v ≡ p'
BY
{ (InstLemma `geo-construction-unicity` [⌜e⌝;⌜O⌝;⌜X⌝;⌜p'⌝;⌜v⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  p'  :  \{p:Point|  O\_X\_p\} 
3.  v  :  Point
4.  [\%2]  :  O\_X\_v  \mwedge{}  Xv  \00D0  Xp'
5.  extend  OX  by  Xp'  =  v
\mvdash{}  v  \mequiv{}  p'


By

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Latex:
(InstLemma  `geo-construction-unicity`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}O\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}p'\mkleeneclose{};\mkleeneopen{}v\mkleeneclose{}]\mcdot{}  THEN  Auto)

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