Lemma

The left pane shows the figure, the givens and the goal. The center is a two-column ledger of statement and justification that you build. From the pool of candidate steps, add one at a time; a step is accepted only when its prerequisites are already proven. Derive the goal to complete the proof.

• Click a candidate step to try adding it to the ledger
• Steps lock until their prerequisite lines are established
• Invalid leaps are rejected, sometimes with a counterexample
• Reach the goal in fewer lines, with fewer hints, for a higher score

• Daily: a fixed proof shared each day
• Practice: fresh randomized problems

• Desktop: click steps in the pool to add them; Undo, Hint and New are on the toolbar
• Phone & tablet: tap a step to add it and tap the toolbar buttons (mouse or touch only)

• Work forward from the givens, look for the step whose prerequisites you already have on the ledger
• Use hints sparingly; each one places the next canonical line but lowers your final score

Lemma teaches rigorous deductive proof, enforcing that every step is justified.

• Skills: deductive proof, formal logic, mathematical rigor
• Best for: advanced high school / college
• For parents & teachers: rigorous deductive proof.

Building a two-column ledger of statement and justification from a pool of candidate steps is the mathematical proof as it is taught in geometry.

Supplying the candidate steps is the original scaffolding.

Offering the steps removes the part that is mostly invention and leaves the part that is mostly logic: deciding what follows from what, and in which order. A step that is true but not yet justified is the characteristic error, and it is only visible in the two-column form.

Lemma is an original free browser logic game that teaches rigorous deductive proof, enforcing that every claim be justified by prior lines just as a real two-column geometry proof demands.

A free, original browser game on PlayPendium. No download, no install.