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.
@article{bwmeta1.element.doi-10_1515_forma-2016-0020, author = {Roland Coghetto}, title = {Homography in RP}, journal = {Formalized Mathematics}, volume = {24}, year = {2016}, pages = {239-251}, zbl = {1357.51021}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0020} }
Roland Coghetto. Homography in ℝℙ. Formalized Mathematics, Tome 24 (2016) pp. 239-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0020/