Lemma

Construct a proof one justified line at a time — every step must follow from what's already on the ledger, and any logical leap is thrown out.

How to play

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

Game modes

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

Controls

• 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)

Tips & strategy

• 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

What you'll learn

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.

About Lemma

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.

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