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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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10 (* \ / This file is distributed under the terms of the *)
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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_sqr.v,v 1.19.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rbasic_fun.ma".
40 Open Local Scope R_scope.
43 (*#***************************************************)
45 (* Rsqr : some results *)
47 (*#***************************************************)
50 Ltac ring_Rsqr := unfold Rsqr in |- *; ring.
53 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_neg.con" as lemma.
55 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_mult.con" as lemma.
57 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_plus.con" as lemma.
59 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_minus.con" as lemma.
61 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_neg_minus.con" as lemma.
63 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_1.con" as lemma.
65 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_gt_0_0.con" as lemma.
67 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_pos_lt.con" as lemma.
69 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_div.con" as lemma.
71 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_eq_0.con" as lemma.
73 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_minus_plus.con" as lemma.
75 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_plus_minus.con" as lemma.
77 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_incr_0.con" as lemma.
79 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_incr_0_var.con" as lemma.
81 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_incr_1.con" as lemma.
83 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_incrst_0.con" as lemma.
85 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_incrst_1.con" as lemma.
87 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_neg_pos_le_0.con" as lemma.
89 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_neg_pos_le_1.con" as lemma.
91 inline procedural "cic:/Coq/Reals/R_sqr/neg_pos_Rsqr_le.con" as lemma.
93 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_abs.con" as lemma.
95 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_le_abs_0.con" as lemma.
97 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_le_abs_1.con" as lemma.
99 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_lt_abs_0.con" as lemma.
101 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_lt_abs_1.con" as lemma.
103 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_inj.con" as lemma.
105 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_eq_abs_0.con" as lemma.
107 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_eq_asb_1.con" as lemma.
109 inline procedural "cic:/Coq/Reals/R_sqr/triangle_rectangle.con" as lemma.
111 inline procedural "cic:/Coq/Reals/R_sqr/triangle_rectangle_lt.con" as lemma.
113 inline procedural "cic:/Coq/Reals/R_sqr/triangle_rectangle_le.con" as lemma.
115 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_inv.con" as lemma.
117 inline procedural "cic:/Coq/Reals/R_sqr/canonical_Rsqr.con" as lemma.
119 inline procedural "cic:/Coq/Reals/R_sqr/Rsqr_eq.con" as lemma.