Step
*
2
of Lemma
geo-lt-angle-in-half-plane-point-exists
1. e : EuclideanPlane
2. w : Point
3. x : Point
4. y : Point
5. z : Point
6. xyz < wyz
7. w leftof yz
8. x leftof yz
9. w leftof yx
10. ∃x@0:Point. (Colinear(y;x;x@0) ∧ w-x@0-z)
⊢ ∃q:Point. (w-q-z ∧ out(y qx))
BY
{ (ExRepD THEN D 0 With ⌜x@0⌝ THEN Auto) }
1
1. e : EuclideanPlane
2. w : Point
3. x : Point
4. y : Point
5. z : Point
6. xyz < wyz
7. w leftof yz
8. x leftof yz
9. w leftof yx
10. x@0 : Point
11. Colinear(y;x;x@0)
12. w-x@0-z
13. w-x@0-z
⊢ out(y x@0x)
Latex:
Latex:
1. e : EuclideanPlane
2. w : Point
3. x : Point
4. y : Point
5. z : Point
6. xyz < wyz
7. w leftof yz
8. x leftof yz
9. w leftof yx
10. \mexists{}x@0:Point. (Colinear(y;x;x@0) \mwedge{} w-x@0-z)
\mvdash{} \mexists{}q:Point. (w-q-z \mwedge{} out(y qx))
By
Latex:
(ExRepD THEN D 0 With \mkleeneopen{}x@0\mkleeneclose{} THEN Auto)
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