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Step * 12 1 of Lemma r2-basic-geo-axioms


∀a,b,x,y,z:ℝ^2.  (r2-left(x;a;b) ⇒ r2-left(y;a;b) ⇒ x_z_y ⇒ r2-left(z;a;b))
BY
{ (Auto THEN InstLemma `r2-left-convex` [⌜a⌝;⌜b⌝;⌜x⌝;⌜z⌝;⌜y⌝]⋅ THEN Auto) }

1
.....antecedent..... 
1. a : ℝ^2
2. b : ℝ^2
3. x : ℝ^2
4. y : ℝ^2
5. z : ℝ^2
6. r2-left(x;a;b)
7. r2-left(y;a;b)
8. x_z_y
⊢ rv-T(2;x;z;y)

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Latex:

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Latex:

\mforall{}a,b,x,y,z:\mBbbR{}\^{}2.    (r2-left(x;a;b)  {}\mRightarrow{}  r2-left(y;a;b)  {}\mRightarrow{}  x\_z\_y  {}\mRightarrow{}  r2-left(z;a;b))


By

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Latex:
(Auto  THEN  InstLemma  `r2-left-convex`  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THEN  Auto)

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