Some Properties of Special Polygonal Curves

In this paper i, j, k, n are natural numbers. The following propositions are true: (1) For all sets A, B, C such that A misses B holds A ∩ (B ∪ C) = A ∩ C. (2) For all sets A, B, C, p such that A ⊆ B and B ∩ C = {p} and p ∈ A holds A ∩ C = {p}. (3) For all real numbers q, r, s, t such that t ­ 0 and t ¬ 1 and s = (1 − t) · q + t · r and q ¬ s and r < s holds t = 0. (4) For all real numbers q, r, s, t such that t ­ 0 and t ¬ 1 and s = (1 − t) · q + t · r and q ­ s and r > s holds t = 0. (5) If i − k ¬ j, then i ¬ j + k.