01
Read a worked proof
See a complete proof with every step justified in the margin.
Pick a track and start.
New to proofs? Take Core. It covers logic and the main proof techniques, one step at a time. You can add more tracks any time, and your progress carries over.
Four steps from reading to writing.
Every skill follows the same path, so you always know what to do next.
02
Fill the gaps
Complete the same proof with blanks where the reasoning goes.
03
Put steps in order
Reorder shuffled steps into a valid argument.
04
Write it yourself
Build a new proof from Assume to Therefore, with hints on request.
Even plus even · Step 4 of 4
Feedback names the step and the rule.
You never get a bare “wrong”. Proofy points to the step to check and the definition that unlocks it, then lets you try again.
Theorem 1.2
Even plus even
If a and b are even integers, then a + b is even.
- 01Let a = 2k and b = 2j.Definition
- 02Then a + b = 2(k + j).Factor out 2
- 03So a + b is even.✕ Gap: no reason given
Not quite
Check step 3: which definition lets you write n = 2k?
25 units.
Open the course01Statements and logic∧ ∨ ¬ ⇒Start here02Truth tablesT FUnit 0203Direct proofP ⇒ QUnit 0304Contrapositive¬Q ⇒ ¬PUnit 0405Contradiction⊥Unit 0506If and only ifP ⇔ QUnit 0607Proof by cases∨Unit 0708Quantifiers∀ ∃Unit 0809SetsA ⊆ BUnit 0910Set identitiesA ∪ BUnit 1011Functionsf: A → BUnit 1112Relationsa ~ bUnit 1213Divisibilitya | bUnit 1314Number theorya ≡ bUnit 1415Inductionn ⇒ n + 1Unit 1516Strong inductionP(1) … P(k)Unit 1617Counting2ⁿUnit 1718Loop invariantswhileUnit 1819Recursion and treesT₁ T₂Unit 1920GraphsG = (V, E)Unit 2021Big-OO(n)Unit 2122Limits of sequencesa(n) → LUnit 2223Choosing a strategy?Unit 2324Writing it well∎Unit 2425Final boss∎∎Unit 25