The Ordering of Points on a Curve. Part I

The following propositions are true: (1) For every natural number i1 such that 1 ¬ i1 holds i1 − ′ 1 < i1. (2) For all natural numbers i, k such that i + 1 ¬ k holds 1 ¬ k − i. (3) For all natural numbers i, k such that 1 ¬ i and 1 ¬ k holds k−i+1 ¬ k. (4) For every real number r such that r ∈ the carrier of I holds 1 − r ∈ the carrier of I. (5) For all points p, q, p1 of E 2 T such that p2 6= q2 and p1 ∈ L(p, q) holds if (p1)2 = p2, then (p1)1 = p1. (6) For all points p, q, p1 of E 2 T such that p1 6= q1 and p1 ∈ L(p, q) holds if (p1)1 = p1, then (p1)2 = p2.