Introduction to Proof Scripting: Basics of Ltac

This lecture covers the fundamentals of proof scripting in Coq, focusing on the Ltac language. The instructor begins by recapping previous concepts and explaining the semantics of the 'match' construct in Ltac, highlighting its backtracking capabilities. The lecture progresses to demonstrate how to structure proofs using bullets and curly braces, which aids in managing multiple goals effectively. The instructor emphasizes the importance of focusing on individual goals to avoid errors during proof development. Various tactics are introduced, including 'try', 'simpl', and 'congruence', showcasing their application in different proof scenarios. The instructor also discusses the use of existential quantifiers and how to handle them within proofs. Throughout the lecture, practical examples illustrate the application of these tactics, emphasizing the need for clarity and organization in proof writing. The session concludes with a discussion on automating repetitive proof steps and the significance of maintaining a structured approach to proof scripting in Coq.