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4 (* ||A|| A project by Andrea Asperti *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec".
19 include "CoRN_notation.ma".
21 (* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
23 (*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
25 include "algebra/CLogic.ma".
30 We prove some basic lemmas of the natural numbers.
32 A variant of [0_S] from the standard library
35 inline "cic:/CoRN/model/structures/Nsec/S_O.con".
40 inline "cic:/CoRN/model/structures/Nsec/ap_nat.con".
42 inline "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con".
44 inline "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con".
46 inline "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con".
48 inline "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con".
53 inline "cic:/CoRN/model/structures/Nsec/plus_strext0.con".
55 (*#* There is no inverse for addition, because every candidate will fail for 2
58 inline "cic:/CoRN/model/structures/Nsec/no_inverse0.con".
60 (*#* ***Multiplication
63 inline "cic:/CoRN/model/structures/Nsec/mult_strext0.con".