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  • 1 Arizona State University West Department of Integrative Studies P.O. Box 37100 Phoenix Az 85069-7100 U.S.A.
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Abstract  

Positive Lω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from [2] by R. Höfer [3].

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