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A constructive and formal proof of Lebesgue's Dominated Convergence Theorem in the interactive theorem prover Matita
, 2008
"... We present a formalisation of a constructive proof of Lebesgue’s Dominated Convergence Theorem given by Sacerdoti Coen and Zoli in [SZ]. The proof is done in the abstract setting of ordered uniformities, also introduced by the two authors as a simplification of Weber’s lattice uniformities given in ..."
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Cited by 7 (4 self)
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We present a formalisation of a constructive proof of Lebesgue’s Dominated Convergence Theorem given by Sacerdoti Coen and Zoli in [SZ]. The proof is done in the abstract setting of ordered uniformities, also introduced by the two authors as a simplification of Weber’s lattice uniformities given in [Web91, Web93]. The proof is fully constructive, in the sense that it is done in Bishop’s style and, under certain assumptions, it is also fully predicative. The formalisation is done in the Calculus of (Co)Inductive Constructions using the interactive theorem prover Matita [ASTZ07]. It exploits some peculiar features of Matita and an advanced technique to represent algebraic hierarchies previously introduced by the authors in [ST07]. Moreover, we introduce a new technique to cope with duality to halve the formalisation effort.
Some considerations on the usability of Interactive Provers
"... Abstract. In spite of the remarkable achievements recently obtained in the field of mechanization of formal reasoning, the overall usability of interactive provers does not seem to be sensibly improved since the advent of the “second generation ” of systems, in the mid of the eighties. We try to ana ..."
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Cited by 3 (1 self)
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Abstract. In spite of the remarkable achievements recently obtained in the field of mechanization of formal reasoning, the overall usability of interactive provers does not seem to be sensibly improved since the advent of the “second generation ” of systems, in the mid of the eighties. We try to analyze the reasons of such a slow progress, pointing out the main problems and suggesting some possible research directions. 1
Formalizing a Proof that e is Transcendental
, 2011
"... We describe a HOL Light formalization of Hermite’s proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover. 1 ..."
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We describe a HOL Light formalization of Hermite’s proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover. 1
The Rooster and the Butterflies
, 2013
"... This paper describes a machinechecked proof of the JordanHölder theorem for finite groups. This purpose of this description is to discuss the representation of the elementary concepts of finite group theory inside type theory. The design choices underlying these representations were crucial to th ..."
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This paper describes a machinechecked proof of the JordanHölder theorem for finite groups. This purpose of this description is to discuss the representation of the elementary concepts of finite group theory inside type theory. The design choices underlying these representations were crucial to the successful formalization of a complete proof of the Odd Order Theorem with the Coq system.