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7 (* ||T|| The HELM team. *)
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15 (* This file was automatically generated: do not edit *********************)
21 (*s Axioms for the basic numerical operations *)
23 include "Num/Params.ma".
25 include "Num/EqAxioms.ma".
27 include "Num/NSyntax.ma".
29 (*s Lemmas for [add] *)
31 inline procedural "cic:/Coq/Num/Nat/Axioms/add_Sx_y.con" as lemma.
34 Hints Resolve add_Sx_y : nat.
37 (*s Lemmas for [add] *)
39 inline procedural "cic:/Coq/Num/Nat/Axioms/add_0_x.con" as lemma.
42 Hints Resolve add_0_x : nat.
45 inline procedural "cic:/Coq/Num/Nat/Axioms/add_sym.con" as lemma.
48 Hints Resolve add_sym : nat.
51 inline procedural "cic:/Coq/Num/Nat/Axioms/add_eq_compat.con" as lemma.
54 Hints Resolve add_eq_compat : nat.
57 inline procedural "cic:/Coq/Num/Nat/Axioms/add_assoc_l.con" as lemma.
59 (*s Lemmas for [one] *)
61 inline procedural "cic:/Coq/Num/Nat/Axioms/S_0_1.con" as lemma.
64 properties of [>], [<=] and [>=] will be derived from [<] *)
66 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_trans.con" as lemma.
69 Hints Resolve lt_trans : nat.
72 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_x_Sx.con" as lemma.
75 Hints Resolve lt_x_Sx : nat.
78 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_S_compat.con" as lemma.
81 Hints Resolve lt_S_compat : nat.
84 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_eq_compat.con" as lemma.
86 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_add_compat_l.con" as lemma.
88 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_Sx_Sy_lt.con" as lemma.
91 Hints Immediate lt_Sx_Sy_lt : nat.
94 inline procedural "cic:/Coq/Num/Nat/Axioms/lt_anti_refl.con" as lemma.