Pascal’s Theorem in Real Projective Plane

In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)¹. Pappus’ theorem is a special case of a degenerate conic of two lines.

For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem². For a lemma, we use PROVER9³ and OTT2MIZ by Josef Urban⁴ [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).