Let The Domain Of Discourse Be The Real Numbers R We Define The Predicate Online

Let the domain of discourse be the real numbers (R). We define the predicate OnLine(a, b, x, y) to be true iff (x, y) lies on the line with slope a and intercept b (i.e. iff ax+b = y) and the predicate InRectangle(u, v, r, s, x, y) to be true iff (x, y) lies inside an r × s rectangle, which has its bottom left corner at (u, v). Prove the following claim:

Should not need to cite any additional facts about geometry, only the definitions given above and possibly some simple algebra. In addition, here are some hints: • To prove that something exists, we can simply demonstrate an object with that property. For example, if we are asked to prove that ∃x (x > 0), we can simply note that 1 > 0. (Formally, the first claim follows from the second by “Intro ∃”, but that step does not need to be explained in an English proof.)

 

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