This paper presents a theoretical analysis of a casebase used for mobile robot path planning in dynamic environments. Unlike other case-based path planning approaches, we use a grid map to represent the environment that permits the robot to operate in unstructured environments. The objective of the mobile robot is to learn to choose paths that are less risky to follow. Our experiments with real robots have shown the efficiency of our concept. In this paper, we replace a heuristic path planning algorithm of the mobile robot with a seed casebase and prove the upper and lower bounds for the cardinality of the casebase. The proofs indicate that it is realistic to seed the casebase with some solutions to a path-finding problem so that no possible solution differs too much from some path in the casebase. This guarantees that the robot would theoretically find all paths from start to goal. The proof of the upper bound of the casebase cardinality shows that the casebase would in a long run grow too large and all possible solutions cannot be stored. In order to keep only the most efficient solutions the casebase has to be revised at run-time or some other measure of path difference has to be considered.