This group gathers theorems of proof theory and entries about how mathematical proofs are built. Proof theory treats proofs themselves as mathematical objects, with results on the elimination of detours, the consistency of arithmetic and the derivation of arithmetic from logic. The group also holds general methods of proof, such as proof by cases, constructive proof and visual proof. A theorem belongs here when its cited article places it in proof theory, metamathematics or the study of how proofs are carried out.
All Proof Theory and Methods of Proof
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Loeb's theorem (Wikipedia)
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In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA.
Cut-elimination theorem
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is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen
Gentzen's consistency proof - Wikipedia
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Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen
Frege's theorem, Wikipedia
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In metalogic and metamathematics, Frege's theorem is a metatheorem
Proof by Exhaustion (Wikipedia)
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Proof by exhaustion, also known as proof by cases
Constructive Proof (Wikipedia)
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In mathematics, a constructive proof is a method of proof that demonstrates the existence
Proof Without Words (Wikipedia)
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In mathematics, a proof without words (or visual proof) is an illustration
Deduction Theorem (Wikipedia)
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theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly
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