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33 (*i $Id: Axioms.v,v 1.6 2002/02/14 14:39:02 filliatr Exp $ i*)
35 (*#* Axioms for the basic numerical operations *)
37 include "Num/Params.ma".
39 include "Num/EqParams.ma".
41 include "Num/NSyntax.ma".
43 (*#* Axioms for [eq] *)
45 inline procedural "cic:/Coq/Num/Axioms/eq_refl.con".
47 inline procedural "cic:/Coq/Num/Axioms/eq_sym.con".
49 inline procedural "cic:/Coq/Num/Axioms/eq_trans.con".
51 (*#* Axioms for [add] *)
53 inline procedural "cic:/Coq/Num/Axioms/add_sym.con".
55 inline procedural "cic:/Coq/Num/Axioms/add_assoc_l.con".
57 inline procedural "cic:/Coq/Num/Axioms/add_0_x.con".
59 (*#* Axioms for [S] *)
61 inline procedural "cic:/Coq/Num/Axioms/add_Sx_y.con".
63 (*#* Axioms for [one] *)
65 inline procedural "cic:/Coq/Num/Axioms/S_0_1.con".
68 properties of [>], [<=] and [>=] will be derived from [<] *)
70 inline procedural "cic:/Coq/Num/Axioms/lt_trans.con".
72 inline procedural "cic:/Coq/Num/Axioms/lt_anti_refl.con".
74 inline procedural "cic:/Coq/Num/Axioms/lt_x_Sx.con".
76 inline procedural "cic:/Coq/Num/Axioms/lt_S_compat.con".
78 inline procedural "cic:/Coq/Num/Axioms/lt_add_compat_l.con".
81 Hints Resolve add_sym add_assoc_l add_0_x add_Sx_y S_0_1 lt_x_Sx lt_S_compat
82 lt_trans lt_anti_refl lt_add_compat_l : num.