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Step * of Lemma eu-add-length_wf

∀[e:EuclideanPlane]. ∀[x,y:{p:Point| O_X_p} ].  (x + y ∈ {p:Point| O_X_p} )
BY
{ (Auto
   THEN (Assert ¬(O = X ∈ Point) BY
               Auto)
   THEN DSetVars
   THEN (Assert ⌜¬(O = x ∈ Point)⌝⋅ THENA (NotEqualFromEuBetween⋅ THEN Auto))) }

1
1. e : EuclideanPlane
2. x : Point
3. O_X_x
4. y : Point
5. O_X_y
6. ¬(O = X ∈ Point)
7. ¬(O = x ∈ Point)
⊢ x + y ∈ {p:Point| O_X_p} 

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Latex:

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Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[x,y:\{p:Point|  O\_X\_p\}  ].    (x  +  y  \mmember{}  \{p:Point|  O\_X\_p\}  )


By

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Latex:
(Auto
  THEN  (Assert  \mneg{}(O  =  X)  BY
                          Auto)
  THEN  DSetVars
  THEN  (Assert  \mkleeneopen{}\mneg{}(O  =  x)\mkleeneclose{}\mcdot{}  THENA  (NotEqualFromEuBetween\mcdot{}  THEN  Auto)))

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