freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / CoRN-Decl / algebra / CGroups.ma

diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma
index d13953b4173d9589a886eb2109e522d0e2f4fcbb..67d508c12fff8abca315b2a9aa0747e26de34b33 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma
@@ -16,6 +16,8 @@
 
 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups".
 
+include "CoRN.ma".
+
 (* $Id: CGroups.v,v 1.9 2004/04/23 10:00:52 lcf Exp $ *)
 
 (*#* printing [-] %\ensuremath-% #−# *)
@@ -26,9 +28,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups".
 
 (*#* printing {--} %\ensuremath-% #−# *)
 
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
 
 (* Begin_SpecReals *)
 
@@ -37,15 +37,17 @@ CMonoids
 ** Definition of the notion of Group
 *)
 
-inline cic:/CoRN/algebra/CGroups/is_inverse.con.
+inline "cic:/CoRN/algebra/CGroups/is_inverse.con".
 
 (* UNEXPORTED
 Implicit Arguments is_inverse [S].
 *)
 
-inline cic:/CoRN/algebra/CGroups/is_CGroup.con.
+inline "cic:/CoRN/algebra/CGroups/is_CGroup.con".
+
+inline "cic:/CoRN/algebra/CGroups/CGroup.ind".
 
-inline cic:/CoRN/algebra/CGroups/CGroup.ind.
+coercion cic:/matita/CoRN-Decl/algebra/CGroups/cg_crr.con 0 (* compounds *).
 
 (* End_SpecReals *)
 
@@ -55,7 +57,11 @@ inline cic:/CoRN/algebra/CGroups/CGroup.ind.
 Implicit Arguments cg_inv [c].
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_minus.con.
+(* NOTATION
+Notation "[--] x" := (cg_inv x) (at level 2, right associativity).
+*)
+
+inline "cic:/CoRN/algebra/CGroups/cg_minus.con".
 
 (*#*
 %\begin{nameconvention}%
@@ -68,6 +74,10 @@ and [ [-] ] with [minus].
 Implicit Arguments cg_minus [G].
 *)
 
+(* NOTATION
+Infix "[-]" := cg_minus (at level 50, left associativity).
+*)
+
 (* End_SpecReals *)
 
 (*#*
@@ -77,15 +87,15 @@ Implicit Arguments cg_minus [G].
 *)
 
 (* UNEXPORTED
-Section CGroup_axioms.
+Section CGroup_axioms
 *)
 
-inline cic:/CoRN/algebra/CGroups/G.var.
+alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var".
 
-inline cic:/CoRN/algebra/CGroups/cg_inverse.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inverse.con".
 
 (* UNEXPORTED
-End CGroup_axioms.
+End CGroup_axioms
 *)
 
 (*#*
@@ -96,79 +106,79 @@ General properties of groups.
 *)
 
 (* UNEXPORTED
-Section CGroup_basics.
+Section CGroup_basics
 *)
 
-inline cic:/CoRN/algebra/CGroups/G.var.
+alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var".
 
-inline cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_minus_correct.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_correct.con".
 
 (* UNEXPORTED
 Hint Resolve cg_rht_inv_unfolded cg_lft_inv_unfolded cg_minus_correct:
   algebra.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_inverse'.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inverse'.con".
 
 (* Hints for Auto *)
 
-inline cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con".
 
 (* UNEXPORTED
 Hint Resolve cg_minus_unfolded: algebra.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_minus_wd.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_wd.con".
 
 (* UNEXPORTED
 Hint Resolve cg_minus_wd: algebra_c.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_minus_strext.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_strext.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con".
 
-inline cic:/CoRN/algebra/CGroups/grp_inv_assoc.con.
+inline "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con".
 
 (* UNEXPORTED
 Hint Resolve grp_inv_assoc: algebra.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_inv.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_inv.con".
 
 (* UNEXPORTED
 Hint Resolve cg_inv_inv: algebra.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_cancel_lft.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_cancel_rht.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique'.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_zero_inv.con.
+inline "cic:/CoRN/algebra/CGroups/cg_zero_inv.con".
 
 (* UNEXPORTED
 Hint Resolve cg_zero_inv: algebra.
 *)
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_zero.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_zero.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_inv_op.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_op.con".
 
 (*#*
 Useful for interactive proof development.
 *)
 
-inline cic:/CoRN/algebra/CGroups/x_minus_x.con.
+inline "cic:/CoRN/algebra/CGroups/x_minus_x.con".
 
 (*#*
 ** Sub-groups
@@ -178,31 +188,31 @@ inline cic:/CoRN/algebra/CGroups/x_minus_x.con.
 *)
 
 (* UNEXPORTED
-Section SubCGroups.
+Section SubCGroups
 *)
 
-inline cic:/CoRN/algebra/CGroups/P.var.
+alias id "P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var".
 
-inline cic:/CoRN/algebra/CGroups/Punit.var.
+alias id "Punit" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var".
 
-inline cic:/CoRN/algebra/CGroups/op_pres_P.var.
+alias id "op_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var".
 
-inline cic:/CoRN/algebra/CGroups/inv_pres_P.var.
+alias id "inv_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var".
 
-inline cic:/CoRN/algebra/CGroups/subcrr.con.
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__".
 
-inline cic:/CoRN/algebra/CGroups/subinv.con.
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__".
 
-inline cic:/CoRN/algebra/CGroups/isgrp_scrr.con.
+inline "cic:/CoRN/algebra/CGroups/isgrp_scrr.con".
 
-inline cic:/CoRN/algebra/CGroups/Build_SubCGroup.con.
+inline "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con".
 
 (* UNEXPORTED
-End SubCGroups.
+End SubCGroups
 *)
 
 (* UNEXPORTED
-End CGroup_basics.
+End CGroup_basics
 *)
 
 (* UNEXPORTED
@@ -228,21 +238,21 @@ Hint Resolve cg_minus_wd: algebra_c.
 *)
 
 (* UNEXPORTED
-Section Assoc_properties.
+Section Assoc_properties
 *)
 
-inline cic:/CoRN/algebra/CGroups/G.var.
+alias id "G" = "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var".
 
-inline cic:/CoRN/algebra/CGroups/assoc_2.con.
+inline "cic:/CoRN/algebra/CGroups/assoc_2.con".
 
-inline cic:/CoRN/algebra/CGroups/zero_minus.con.
+inline "cic:/CoRN/algebra/CGroups/zero_minus.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con".
 
-inline cic:/CoRN/algebra/CGroups/plus_resp_eq.con.
+inline "cic:/CoRN/algebra/CGroups/plus_resp_eq.con".
 
 (* UNEXPORTED
-End Assoc_properties.
+End Assoc_properties
 *)
 
 (* UNEXPORTED
@@ -258,35 +268,35 @@ Specific properties of apartness.
 *)
 
 (* UNEXPORTED
-Section cgroups_apartness.
+Section cgroups_apartness
 *)
 
-inline cic:/CoRN/algebra/CGroups/G.var.
+alias id "G" = "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var".
 
-inline cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con".
 
-inline cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con.
+inline "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con".
 
-inline cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con.
+inline "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con".
 
-inline cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con".
 
-inline cic:/CoRN/algebra/CGroups/minus_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/minus_ap_zero.con".
 
-inline cic:/CoRN/algebra/CGroups/zero_minus_apart.con.
+inline "cic:/CoRN/algebra/CGroups/zero_minus_apart.con".
 
-inline cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con".
 
-inline cic:/CoRN/algebra/CGroups/inv_resp_ap.con.
+inline "cic:/CoRN/algebra/CGroups/inv_resp_ap.con".
 
-inline cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con".
 
-inline cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con.
+inline "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con".
 
-inline cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con".
 
 (* UNEXPORTED
-End cgroups_apartness.
+End cgroups_apartness
 *)
 
 (* UNEXPORTED
@@ -298,7 +308,7 @@ Hint Resolve minus_ap_zero zero_minus_apart inv_resp_ap_zero: algebra.
 *)
 
 (* UNEXPORTED
-Section CGroup_Ops.
+Section CGroup_Ops
 *)
 
 (*#*
@@ -312,42 +322,42 @@ by [P] and [Q].
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CGroups/G.var.
+alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var".
 
-inline cic:/CoRN/algebra/CGroups/F.var.
+alias id "F" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var".
 
-inline cic:/CoRN/algebra/CGroups/F'.var.
+alias id "F'" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/algebra/CGroups/P.con.
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__".
 
-inline cic:/CoRN/algebra/CGroups/Q.con.
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__".
 
 (* end hide *)
 
 (* UNEXPORTED
-Section Part_Function_Inv.
+Section Part_Function_Inv
 *)
 
-inline cic:/CoRN/algebra/CGroups/part_function_inv_strext.con.
+inline "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con".
 
-inline cic:/CoRN/algebra/CGroups/Finv.con.
+inline "cic:/CoRN/algebra/CGroups/Finv.con".
 
 (* UNEXPORTED
-End Part_Function_Inv.
+End Part_Function_Inv
 *)
 
 (* UNEXPORTED
-Section Part_Function_Minus.
+Section Part_Function_Minus
 *)
 
-inline cic:/CoRN/algebra/CGroups/part_function_minus_strext.con.
+inline "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con".
 
-inline cic:/CoRN/algebra/CGroups/Fminus.con.
+inline "cic:/CoRN/algebra/CGroups/Fminus.con".
 
 (* UNEXPORTED
-End Part_Function_Minus.
+End Part_Function_Minus
 *)
 
 (*#*
@@ -355,30 +365,38 @@ End Part_Function_Minus.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CGroups/R.var.
+alias id "R" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var".
 
-inline cic:/CoRN/algebra/CGroups/included_FInv.con.
+inline "cic:/CoRN/algebra/CGroups/included_FInv.con".
 
-inline cic:/CoRN/algebra/CGroups/included_FInv'.con.
+inline "cic:/CoRN/algebra/CGroups/included_FInv'.con".
 
-inline cic:/CoRN/algebra/CGroups/included_FMinus.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus.con".
 
-inline cic:/CoRN/algebra/CGroups/included_FMinus'.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus'.con".
 
-inline cic:/CoRN/algebra/CGroups/included_FMinus''.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus''.con".
 
 (* UNEXPORTED
-End CGroup_Ops.
+End CGroup_Ops
 *)
 
 (* UNEXPORTED
 Implicit Arguments Finv [G].
 *)
 
+(* NOTATION
+Notation "{--} x" := (Finv x) (at level 2, right associativity).
+*)
+
 (* UNEXPORTED
 Implicit Arguments Fminus [G].
 *)
 
+(* NOTATION
+Infix "{-}" := Fminus (at level 50, left associativity).
+*)
+
 (* UNEXPORTED
 Hint Resolve included_FInv included_FMinus : included.
 *)