Affiliation:
1. Rue de la Brasserie 5, 7100 La Louvière, Belgium
Abstract
Summary
The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12].
Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18].
In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17].
Then we show that the projective space induced (in the sense defined in [9]) by ℝ3 is a projective plane (in the sense defined in [10]).
Finally, in the real projective plane, we define the homography induced by a 3-by-3 invertible matrix and we show that the images of 3 collinear points are themselves collinear.
Subject
Applied Mathematics,Computational Mathematics
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