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Step * 1 of Lemma geo-sep-iff-or-lt


1. e : BasicGeometry
2. x : {p:Point| O_X_p} 
3. y : {p:Point| O_X_p} 
4. x ≠ y
⊢ x < y ∨ y < x
BY
{ ((InstLemma `geo-between-same-side-or` [⌜e⌝;⌜O⌝;⌜X⌝;⌜x⌝;⌜y⌝]⋅ THENA Auto) THEN ParallelLast THEN Auto) }

1
1. e : BasicGeometry
2. x : {p:Point| O_X_p} 
3. y : {p:Point| O_X_p} 
4. x ≠ y
5. O_x_y
⊢ x < y

2
1. e : BasicGeometry
2. x : {p:Point| O_X_p} 
3. y : {p:Point| O_X_p} 
4. x ≠ y
5. O_y_x
⊢ y < x

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Latex:

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Latex:

1.  e  :  BasicGeometry
2.  x  :  \{p:Point|  O\_X\_p\} 
3.  y  :  \{p:Point|  O\_X\_p\} 
4.  x  \mneq{}  y
\mvdash{}  x  <  y  \mvee{}  y  <  x


By

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Latex:
((InstLemma  `geo-between-same-side-or`  [\mkleeneopen{}e\mkleeneclose{};\mkleeneopen{}O\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  ParallelLast
  THEN  Auto)

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