Explain how goal trees are useful in theorem proving?

Goal trees are useful in theorem proving as they provide a structured way to break down complex theorems into simpler sub-goals. By representing the proof as a tree, each node corresponds to a goal that needs to be proven, enabling systematic exploration of different proof strategies. This hierarchical approach helps identify dependencies between goals and allows for efficient backtracking when certain branches do not lead to a solution. Ultimately, goal trees enhance clarity and organization in the theorem proving process.