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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: R_sqrt.v,v 1.10.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/Rsqrt_def.ma".
42 Open Local Scope R_scope.
45 (* Here is a continuous extension of Rsqrt on R *)
47 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt.con" as definition.
49 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_positivity.con" as lemma.
51 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_sqrt.con" as lemma.
53 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_0.con" as lemma.
55 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_1.con" as lemma.
57 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_eq_0.con" as lemma.
59 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lem_0.con" as lemma.
61 inline procedural "cic:/Coq/Reals/R_sqrt/sqtr_lem_1.con" as lemma.
63 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_def.con" as lemma.
65 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_square.con" as lemma.
67 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_Rsqr.con" as lemma.
69 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_Rsqr_abs.con" as lemma.
71 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sqrt.con" as lemma.
73 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_mult.con" as lemma.
75 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_R0.con" as lemma.
77 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_div.con" as lemma.
79 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_0.con" as lemma.
81 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_1.con" as lemma.
83 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_le_0.con" as lemma.
85 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_le_1.con" as lemma.
87 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_inj.con" as lemma.
89 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_less.con" as lemma.
91 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_more.con" as lemma.
93 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_cauchy.con" as lemma.
95 (*#***********************************************************)
97 (* Resolution of [a*X^2+b*X+c=0] *)
99 (*#***********************************************************)
101 inline procedural "cic:/Coq/Reals/R_sqrt/Delta.con" as definition.
103 inline procedural "cic:/Coq/Reals/R_sqrt/Delta_is_pos.con" as definition.
105 inline procedural "cic:/Coq/Reals/R_sqrt/sol_x1.con" as definition.
107 inline procedural "cic:/Coq/Reals/R_sqrt/sol_x2.con" as definition.
109 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sol_eq_0_1.con" as lemma.
111 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sol_eq_0_0.con" as lemma.