Simplifying the axiomatization for the ordered affine geometry via a theorem prover

Abstract

Based on an ordering with directed lines and using constructions instead of existential axioms, von Plato proposed a constructive axiomatization of the ordered affine geometry. There are 22 axioms for the ordered affine geometry, of which the axiom I.7 is about the convergence of three lines (ignoring their directions). In this paper, we indicate that the axiom I.7 includes much redundancy, and demonstrate that the complicated axiom I.7 can be replaced equivalently with a simpler and more intuitive new axiom via a theorem prover.