Exercise sheet L-c -- Disjunction

Interactive Theorem Proving using Lean — Exercise sheet L-c University of Freiburg, winter term 2026/27 The third exercise sheet, solved from start to finish: disjunction. How to prove P ∨ Q by choosing a side, how to use a hypothesis P ∨ Q by handling both cases, and the two distributive laws between ∧ and ∨. Everything on this sheet is provable constructively. Exercise sheet: https://github.com/pfaffelh/leancourse_exe... All sheets: https://github.com/pfaffelh/leancourse_exe... Course notes: https://pfaffelh.github.io/leancourse/ Proof game: https://pfaffelh.github.io/ipm Lean: https://lean-lang.org/ Mathlib: https://leanprover-community.github.io/ No local installation? The sheet also runs in the browser: https://live.lean-lang.org/#project=mathli... TACTICS USED left, right, Or.inl and Or.inr, obtain (h1 | h2). CHAPTERS 00:00 What this sheet is about 00:15 The sheet and its tactics table 01:00 Proving an ∨ 01:30 How Or is defined in Lean 02:15 Exercise 1 02:30 Exercise 2 03:00 Using an ∨ hypothesis 03:45 Exercise 3 04:00 Exercise 4 07:45 Exercise 5 08:30 Exercise 6 09:45 Distributivity, Exercise 7a 13:15 Exercise 7b 16:15 Exercise 8 18:30 Exercise 9