5. Lecture 5: Forward Proofs
Lecture 4 proved the theorems of logic backwards, starting at the goal and reducing it with tactics. This lecture turns the same statements around and proves them forwards, starting at the hypotheses and deriving new facts until it reaches the goal, following chapter 4 of the Hitchhiker's Guide to Logical Verification.A. Baanen, A. Bentkamp, J. Blanchette, J. Hölzl, J. Limperg, The Hitchhiker's Guide to Logical Verification, 2026 edition, chapter 4. It writes proofs as structured terms whose shape mirrors the proposition, it introduces calculational proofs with calc, and it explains the Curry–Howard reading, the principle that a proof is a term and a proposition is a type. These are the two faces of one activity, and by the end the two lectures read as a single argument seen from both ends.
This lecture is also available as presentation slides.