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Questions tagged [proof-golf]

Proof-golf is a competition to prove a particular theorem/statement using the fewest number of substitutions/steps given a set of axioms.

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122
votes
11answers
12k views

(-a) × (-a) = a × a

We all know that \$(-a) \times (-a) = a \times a\$ (hopefully), but can you prove it? Your task is to prove this fact using the ring axioms. What are the ring axioms? The ring axioms are a list of ...
38
votes
3answers
1k views

(A → B) → (¬B → ¬A)

Well I think it is about time we have another proof-golf question. This time we are going to prove the well known logical truth \$(A \rightarrow B) \rightarrow (\neg B \rightarrow \neg A)\$ To do ...
21
votes
2answers
498 views

Existential Golf

Math has a lot of symbols. Some might say too many symbols. So lets do some math with pictures. Lets have a paper, which we will draw on. To start the paper is empty, we will say that is ...
21
votes
3answers
737 views

Prove DeMorgan's laws

Using the the ten inferences of the Natural Deduction System prove DeMorgan's laws. The Rules of Natural Deduction Negation Introduction: {(P → Q), (P → ¬Q)} ⊢ ¬P ...