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'''Logical relations''' are a [[proof method]] employed in [[programming language semantics]] to show that two [[ ...oaded]: Proofs involving logical relations used as a benchmark for [[proof assistants]]. ...

...lver]]s, [[SMT solver|SMT-solvers]], [[first-order theorem provers]] and [[proof assistant]]s. ...elements of ''C'', the resolvent nodes are resolution inferences, and the proof has a node with conclusion <math>\kappa</math>.<ref name="Compression of Pr ...

...onard Eugene Dickson]], John Knopfmacher, and Wayne L. McDaniel. Dickson's proof, in particular, has been commonly used in textbooks.<ref>{{citation|last=Co ...proof of the Euclid–Euler theorem had been formalized in 7 of the 12 proof assistants recorded by Wiedijk.<ref>{{citation|first=Freek|last=Wiedijk|url=https://ww ...

...roof of an equality <math>x = x</math> is equal to the trivial reflexivity proof. ...actice in [[proof assistants]] because it removes parts of proofs from the proof terms. ...

{{short description|Proof assistant and programming language}} | family = [[Proof assistant]] ...

Unlike many other formulations of type theory and proof assistants based on ...= An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof ...

...le); and the [[Formal proof|formalization]] of each of these in computer [[proof assistant]]s. ...start developing significant amounts of "synthetic homotopy theory" in the proof assistant [[Coq (software)|Coq]]; this formed the basis of the library late ...

...].<ref name=Frohlich/> In retrospect, this insistence and the style of his proof initiated the modern particle-physics era, where abstract quantum propertie {{math proof ...

...[[axiomatic system]] and the first examples of [[Mathematical proof|formal proof]]. It goes on to the [[solid geometry]] of [[three dimensions]]. Much of th ...ompass and straightedge constructions|constructions]]), and [[mathematical proof]]s of the propositions. The thirteen books cover [[Euclidean geometry]] and ...

Most of the students, laboratory assistants and technicians had been called up, so Hahn, who was stationed in Berlin be ...time for research, as administration was devolved to Hahn's and Meitner's assistants.{{sfn|Sime|1996|pp=156–157, 169}} ...

...iting proofs in natural language, though benchmarking proofs in a [[Formal proof|formal language]] is possible. ...ion |last1=Mialon |first1=Grégoire |title=GAIA: a benchmark for General AI Assistants |date=2023-11-21 |arxiv=2311.12983 |last2=Fourrier |first2=Clémentine |last ...

...ess, inevitability'', and ''economy''" (King's italics), and describes the proof as "aesthetically pleasing".<ref>{{cite book |last=King |first=Jerry P. |ti ...p the triptych as an offering.<ref>{{cite web |title=Giotto di Bondone and assistants: Stefaneschi triptych |url=http://mv.vatican.va/3_EN/pages/PIN/PIN_Sala02_0 ...

...important passages in the messages were underscored by Kalckstein and his assistants. Fenner objected to this ''predigestion'' owing to the danger that the read The examination was a [[Pro forma]] matter, as it called for proof of real knowledge and ability. Both examiner and examinee were expected to ...

...edical and [[dental assistant]]s (then called medical assistants or dental assistants) received this additional training in 1990.<ref name=":1">Petra Sonja Geyer ...d been converted at great expense in the early 1960s into a nuclear-weapon-proof building. However, it would be impossible to build a bunker for millions of ...

...bbin|2002|p=101}}{{sfn|Ferguson|2011|pp=61, 64}} In 1970, they published a proof that if the universe obeys [[general relativity|the general theory of relat ...whelmed by the intrusion into their family life of the required nurses and assistants.{{sfn|Ferguson|2011|pp=164–65}} The impact of his celebrity status was chal ...