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Summary: Verification of Newman's and Yokouchi's Lemmas in PVS
Andr´e Luiz Galdino1,2
, Mauricio Ayala-Rinc´on1
1
Grupo de Teoria da Computac¸~ao
Instituto de Ci^encias Exatas Universidade de Bras´ilia
Bras´ilia, Brazil
2
Departamento de Matem´atica Campus de Catal~ao Universidade Federal de Goi´as
Catal~ao, Brazil
{galdino,ayala}@unb.br
Abstract. This paper shows how a previously specified theory for Abstract Re-
duction Systems (ARSs) in which noetherianity was defined by the notion of well-
foundness over binary relations is used in order to prove results such as the well-
known Newman's Lemma and the Yokouchi's Lemma. The former one known as
the diamond lemma and the later which states a property of commutation be-
tween ARSs. The ars theory was specified in the Prototype Verification System
(PVS) for which to the best of our knowledge there are no available theory for
dealing with rewriting techniques in general. In addition to proof techniques
available in PVS the verification of these lemmas implies an elaborated use of
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