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4 (* ||A|| A project by Andrea Asperti *)
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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
21 (*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
23 include "algebra/CLogic.ma".
28 We prove some basic lemmas of the natural numbers.
30 A variant of [0_S] from the standard library
33 inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con" as lemma.
38 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con" as definition.
41 Infix "{#N}" := ap_nat (no associativity, at level 90).
44 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con" as lemma.
46 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con" as lemma.
48 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con" as lemma.
50 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con" as lemma.
55 inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con" as lemma.
57 (*#* There is no inverse for addition, because every candidate will fail for 2
60 inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con" as lemma.
62 (*#* ***Multiplication
65 inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con" as lemma.