Prover-agnostic. Pen-and-paper to Lean 4.
Start with pure logic in Gentzen notation — no tools required. Then move to real theorem provers. You don't understand a theorem until you've proved it yourself.
Each exercise explains the concept — what the theorem means, why it matters, and the intuition behind it.
Watch the proof unfold — as a Gentzen inference tree or as tactic steps. See hypotheses appear, goals narrow, subgoals split. Understand why each step works.
Try it yourself — draw the inference tree on paper, or paste into Lean 4 Web. If you can build the tree or Lean accepts it, you've proved it.
Each track is a sequence of lessons and exercises, ordered by difficulty. Learn the maths, then prove it.
Natural deduction from scratch. Gentzen's inference rules — the universal language beneath every theorem prover.
9 exercisesPropositional logic, implications, if-and-only-if, negation, classical reasoning.
6 exercisesPeano axioms, induction, addition, multiplication, ordering.
5 exercisesHow to choose tactics. Direct proof, case analysis, contradiction, induction, rewriting.
8 exercisesMembership, subsets, union, intersection, complements, power sets.
coming soonInjectivity, surjectivity, composition, inverse functions.
coming soonGroups, rings, homomorphisms, quotients.
coming soonLimits, continuity, sequences, series, the reals.
coming soonNone beyond basic arithmetic. We teach the maths as we go. That's the point.
Helpful but not required. If you've used any programming language, Lean's syntax will feel familiar.
For Proof Theory: just pen and paper. For Lean exercises: use Lean 4 Web in your browser, or install Lean 4 + VS Code locally for a better experience.