1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CVectorSpace".
21 (* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *)
23 (*#* printing ['] %{'}% #'# *)
25 include "algebra/CFields.ma".
30 Obsolete but maintained.
36 Set Implicit Arguments.
40 Unset Strict Implicit.
45 inline "cic:/CoRN/algebra/CVectorSpace/VSpace.ind".
47 coercion cic:/matita/CoRN-Decl/algebra/CVectorSpace/vs_vs.con 0 (* compounds *).
56 Unset Implicit Arguments.
62 Hint Resolve vs_assoc vs_unit vs_distl vs_distr: algebra.
66 Implicit Arguments vs_op [F v].
70 Infix "[']" := vs_op (at level 30, no associativity).
75 Let [F] be a fiels and let [V] be a vector space over [F]
83 alias id "F" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var".
85 alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var".
87 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con".
89 inline "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con".
92 Hint Resolve vs_op_zero zero_vs_op: algebra.
95 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con".
97 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con".
100 Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
103 inline "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con".
106 Hint Resolve vs_inv_assoc: algebra.
109 inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con".
111 inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con".
113 (* note this is the same proof as mult_resp_ap_zero *)
115 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con".
117 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con".
119 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con".
126 Hint Resolve vs_op_zero zero_vs_op: algebra.