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...' ({{Langx|de|Beweis durch Ringschluss|lit=Proof by ring-inference}}) is a mathematical [[Proof (mathematics)|proof]] technique where the equivalence of several st ...ents <math>\varphi_1,\ldots,\varphi_n</math> are each pairwise equivalent, proofs are given for the implications <math>\varphi_1\Rightarrow\varphi_2</math>, ...

{{Short description|Mathematical analysis theorem}} In mathematical analysis, '''Tannery's theorem''' gives sufficient conditions for the [[Int ...

In the [[mathematics|mathematical]] theory of [[Lie group]]s, the '''Chevalley restriction theorem''' describ ==Proofs== ...

....<ref name=Cotton>Cotton, Scott. "Two Techniques for Minimizing Resolution Proofs". 13th International Conference on Theory and Applications of Satisfiabilit ...th> and a proof of <math>\neg x </math> and the recombination of these two proofs (by an additional resolution step) may result in a proof smaller than the o ...

...ing [[formal proof]]s. The developed algorithms can be used to improve the proofs generated by [[automated theorem proving]] tools such as [[SAT solver]]s, [ ...ion <math>\kappa</math>.<ref name="Compression of Propositional Resolution Proofs via Partial Regularization"/> ...

In [[mathematical analysis]], the '''initial value theorem''' is a theorem used to relate [[f == Proofs == ...

...a positive evaluation, saying that he "learned something new" from several proofs and found some of them quite comedic.<ref>{{cite web|first=Geoffrey |last=D ...

| name = Proofs That Really Count: the Art of Combinatorial Proof ...thematical Expositions series. It won the [[Beckenbach Book Prize]] of the Mathematical Association of America. ...

{{Short description|Mathematical inequality}} ...r Engel (mathematician)|Arthur Engel]] published in 1998 and to the book ''Mathematical Olympiad Treasures'' of [[Titu Andreescu]] published in 2003.<ref name="Alg ...

==Proofs== ===Inductive and algebraic proofs=== ...

...oc/2010-138-11/S0002-9939-10-10380-3/ |journal=Proceedings of the American Mathematical Society |language=en |volume=138 |issue=11 |pages=3945–3955 |doi=10.1090/S0 == Statements and proofs == ...

{{Short description|1876 mathematical proof by the US president}} ...00loom_b2m3 |access-date=28 November 2023}} (A collection of 370 different proofs of the Pythagorean theorem.)</ref> ...

...phan; Woltzenlogel Paleo, Bruno. ''Compression of Propositional Resolution Proofs via Partial Regularization''. 23rd International Conference on Automated De ...globally) redundant if it can be rewritten to one of the following shorter proofs: ...

{{Short description|Mathematical proof expressed visually}} ...matical beauty|elegant]] than formal or [[rigour|mathematically rigorous]] proofs due to their self-evident nature.<ref name="dunham120">{{Harvnb|Dunham|1994 ...

...) is a possible axiom for dependent type theory which asserts that any two proofs of the same equality are themselves equal. An equivalent and closely relate ...s not used in practice in [[proof assistants]] because it removes parts of proofs from the proof terms. ...

==Proofs== ...doi=10.1307/mmj/1029003189 | mr=783576 | year=1985 | journal=The Michigan Mathematical Journal | issn=0026-2285 | volume=32 | issue=2 | pages=221–225 | zbl=0569.1 ...

...tle=Li Shanlan (1811–1882) and Chinese Traditional Mathematics|journal=The Mathematical Intelligencer|date=September 1992|volume=14|issue=4|pages=32–37|doi=10.1007 ==Proofs of the identity== ...

...=1930|title=Sur une inégalité intégrale|periodical=[[Journal of the London Mathematical Society]]|volume=5|issue=3 |pages=162–168|doi=10.1112/jlms/s1-5.3.162|mr=15 == Proofs == ...

...mber]], and let <math>s\in (0,1)</math>. Then,<ref>NIST Digital Library of Mathematical Functions, 5.6.4.</ref> ==Proofs== ...

...= Frank Pfenning|last4=Scedrov|first4=Andre|date=1991-03-14|title=Uniform proofs as a foundation for logic programming|journal=[[Annals of Pure and Applied ...or [[System LK]], [[System LJ]], and System LL, uniform proofs are focused proofs where all the atoms are assigned negative polarity.<ref>{{Cite journal|last ...