Cell Petri Net Concepts

Let A be a non empty set, let B be a set, let B1 be a set, and let y1 be a function from B1 into A. Let us assume that B1 ⊆ B. The functor cylinder0(A,B,B1, y1) yields a non empty subset of A B and is defined by: (Def. 1) cylinder0(A,B,B1, y1) = {y : B → A: y B1 = y1}. Let A be a non empty set and let B be a set. A non empty subset of AB is said to be a thin cylinder of A and B if: (Def. 2) There exists a subset B1 of B and there exists a function y1 from B1 into A such that B1 is finite and it = cylinder0(A,B,B1, y1). The following propositions are true: