- new library/logic/coimplication.ma uses new decompose tactic

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

diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma
index 9210cad60b7c2cd6bc6ecd79f79592719f9921fa..64f84532b806eb0a497a1b84f2e81eef4eb6d09a 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma
@@ -16,7 +16,7 @@
 
 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings".
 
-include "CoRN_notation.ma".
+include "CoRN.ma".
 
 (* $Id: CRings.v,v 1.8 2004/04/23 10:00:53 lcf Exp $ *)
 
@@ -83,7 +83,7 @@ inline "cic:/CoRN/algebra/CRings/is_CRing.ind".
 
 inline "cic:/CoRN/algebra/CRings/CRing.ind".
 
-coercion "cic:/matita/CoRN-Decl/algebra/CRings/cr_crr.con" 0 (* compounds *).
+coercion cic:/matita/CoRN-Decl/algebra/CRings/cr_crr.con 0 (* compounds *).
 
 inline "cic:/CoRN/algebra/CRings/cr_plus.con".
 
@@ -91,6 +91,10 @@ inline "cic:/CoRN/algebra/CRings/cr_inv.con".
 
 inline "cic:/CoRN/algebra/CRings/cr_minus.con".
 
+(* NOTATION
+Notation One := (cr_one _).
+*)
+
 (* End_SpecReals *)
 
 (* Begin_SpecReals *)
@@ -106,8 +110,12 @@ and [[*]] with [mult].
 Implicit Arguments cr_mult [c].
 *)
 
+(* NOTATION
+Infix "[*]" := cr_mult (at level 40, left associativity).
+*)
+
 (* UNEXPORTED
-Section CRing_axioms.
+Section CRing_axioms
 *)
 
 (*#*
@@ -116,7 +124,7 @@ Section CRing_axioms.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/CRing_axioms/R.var" "CRing_axioms__".
 
 inline "cic:/CoRN/algebra/CRings/CRing_is_CRing.con".
 
@@ -141,11 +149,11 @@ inline "cic:/CoRN/algebra/CRings/mult_wdr.con".
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-End CRing_axioms.
+End CRing_axioms
 *)
 
 (* UNEXPORTED
-Section Ring_constructions.
+Section Ring_constructions
 *)
 
 (*#*
@@ -155,7 +163,7 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_constructions/R.var" "Ring_constructions__".
 
 (*#*
 The multiplicative monoid of a ring is defined as follows.
@@ -164,13 +172,13 @@ The multiplicative monoid of a ring is defined as follows.
 inline "cic:/CoRN/algebra/CRings/Build_multCMonoid.con".
 
 (* UNEXPORTED
-End Ring_constructions.
+End Ring_constructions
 *)
 
 (* End_SpecReals *)
 
 (* UNEXPORTED
-Section Ring_unfolded.
+Section Ring_unfolded
 *)
 
 (*#*
@@ -179,11 +187,11 @@ Section Ring_unfolded.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var" "Ring_unfolded__".
 
 (* begin hide *)
 
-inline "cic:/CoRN/algebra/CRings/mmR.con".
+inline "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__".
 
 (* end hide *)
 
@@ -208,7 +216,7 @@ Hint Resolve ring_dist_unfolded: algebra.
 inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con".
 
 (* UNEXPORTED
-End Ring_unfolded.
+End Ring_unfolded
 *)
 
 (* UNEXPORTED
@@ -224,7 +232,7 @@ Hint Resolve ring_dist_unfolded ring_distl_unfolded: algebra.
 *)
 
 (* UNEXPORTED
-Section Ring_basics.
+Section Ring_basics
 *)
 
 (*#*
@@ -233,7 +241,7 @@ Section Ring_basics.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_basics/R.var" "Ring_basics__".
 
 inline "cic:/CoRN/algebra/CRings/one_ap_zero.con".
 
@@ -294,7 +302,7 @@ Hint Resolve ring_distl_minus: algebra.
 *)
 
 (* UNEXPORTED
-End Ring_basics.
+End Ring_basics
 *)
 
 (* UNEXPORTED
@@ -326,7 +334,7 @@ especially geared towards CReals.
 *)
 
 (* UNEXPORTED
-Section exponentiation.
+Section exponentiation
 *)
 
 (*#*
@@ -336,7 +344,7 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/exponentiation/R.var" "exponentiation__".
 
 (* End_SpecReals *)
 
@@ -351,11 +359,15 @@ inline "cic:/CoRN/algebra/CRings/nexp_op.con".
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-End exponentiation.
+End exponentiation
 *)
 
 (* End_SpecReals *)
 
+(* NOTATION
+Notation "x [^] n" := (nexp_op _ n x) (at level 20).
+*)
+
 (* UNEXPORTED
 Implicit Arguments nexp_op [R].
 *)
@@ -363,7 +375,7 @@ Implicit Arguments nexp_op [R].
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-Section nat_injection.
+Section nat_injection
 *)
 
 (*#*
@@ -372,7 +384,7 @@ Section nat_injection.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/nat_injection/R.var" "nat_injection__".
 
 (*#*
 The injection of Coq natural numbers into a ring is called [nring].
@@ -393,7 +405,7 @@ inline "cic:/CoRN/algebra/CRings/nring_comm_mult.con".
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-End nat_injection.
+End nat_injection
 *)
 
 (* End_SpecReals *)
@@ -410,6 +422,50 @@ Implicit Arguments nring [R].
 
 (* End_SpecReals *)
 
+(* NOTATION
+Notation Two := (nring 2).
+*)
+
+(* NOTATION
+Notation Three := (nring 3).
+*)
+
+(* NOTATION
+Notation Four := (nring 4).
+*)
+
+(* NOTATION
+Notation Six := (nring 6).
+*)
+
+(* NOTATION
+Notation Eight := (nring 8).
+*)
+
+(* NOTATION
+Notation Twelve := (nring 12).
+*)
+
+(* NOTATION
+Notation Sixteen := (nring 16).
+*)
+
+(* NOTATION
+Notation Nine := (nring 9).
+*)
+
+(* NOTATION
+Notation Eighteen := (nring 18).
+*)
+
+(* NOTATION
+Notation TwentyFour := (nring 24).
+*)
+
+(* NOTATION
+Notation FortyEight := (nring 48).
+*)
+
 inline "cic:/CoRN/algebra/CRings/one_plus_one.con".
 
 inline "cic:/CoRN/algebra/CRings/x_plus_x.con".
@@ -425,7 +481,7 @@ In a ring of characteristic zero, [nring] is really an injection.
 inline "cic:/CoRN/algebra/CRings/nring_different.con".
 
 (* UNEXPORTED
-Section int_injection.
+Section int_injection
 *)
 
 (*#*
@@ -435,7 +491,7 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/int_injection/R.var" "int_injection__".
 
 (*#*
 The injection of Coq integers into a ring is called [zring]. Again,
@@ -565,7 +621,7 @@ inline "cic:/CoRN/algebra/CRings/zring_one.con".
 inline "cic:/CoRN/algebra/CRings/zring_inv_one.con".
 
 (* UNEXPORTED
-End int_injection.
+End int_injection
 *)
 
 (* UNEXPORTED
@@ -579,7 +635,7 @@ Hint Resolve pring_convert zring_zero zring_diff zring_plus_nat zring_inv_nat
 *)
 
 (* UNEXPORTED
-Section Ring_sums.
+Section Ring_sums
 *)
 
 (*#*
@@ -588,14 +644,14 @@ Section Ring_sums.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_sums/R.var" "Ring_sums__".
 
 (*#*
 *** Infinite Ring sums
 *)
 
 (* UNEXPORTED
-Section infinite_ring_sums.
+Section infinite_ring_sums
 *)
 
 inline "cic:/CoRN/algebra/CRings/Sum_upto.con".
@@ -614,11 +670,11 @@ inline "cic:/CoRN/algebra/CRings/seq_from.con".
 inline "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con".
 
 (* UNEXPORTED
-End infinite_ring_sums.
+End infinite_ring_sums
 *)
 
 (* UNEXPORTED
-Section ring_sums_over_lists.
+Section ring_sums_over_lists
 *)
 
 (*#* *** Ring Sums over Lists
@@ -633,11 +689,11 @@ inline "cic:/CoRN/algebra/CRings/list_sum_upto_O.con".
 inline "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con".
 
 (* UNEXPORTED
-End ring_sums_over_lists.
+End ring_sums_over_lists
 *)
 
 (* UNEXPORTED
-End Ring_sums.
+End Ring_sums
 *)
 
 (*#*
@@ -648,10 +704,10 @@ Let [R] be a ring.
 *)
 
 (* UNEXPORTED
-Section Dist_properties.
+Section Dist_properties
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Dist_properties/R.var" "Dist_properties__".
 
 inline "cic:/CoRN/algebra/CRings/dist_1b.con".
 
@@ -688,7 +744,7 @@ inline "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con".
 inline "cic:/CoRN/algebra/CRings/sumx_const.con".
 
 (* UNEXPORTED
-End Dist_properties.
+End Dist_properties
 *)
 
 (* UNEXPORTED
@@ -704,10 +760,10 @@ Let [R] be a ring.
 *)
 
 (* UNEXPORTED
-Section NExp_properties.
+Section NExp_properties
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/NExp_properties/R.var" "NExp_properties__".
 
 inline "cic:/CoRN/algebra/CRings/nexp_wd.con".
 
@@ -808,7 +864,7 @@ Hint Resolve nexp_funny': algebra.
 *)
 
 (* UNEXPORTED
-End NExp_properties.
+End NExp_properties
 *)
 
 (* UNEXPORTED
@@ -819,7 +875,7 @@ Hint Resolve nexp_wd nexp_Sn nexp_plus one_nexp mult_nexp nexp_mult zero_nexp
 *)
 
 (* UNEXPORTED
-Section CRing_Ops.
+Section CRing_Ops
 *)
 
 (*#*
@@ -833,22 +889,22 @@ respectively [P] and [Q].
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/R.var" "CRing_Ops__".
 
-inline "cic:/CoRN/algebra/CRings/F.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/F.var" "CRing_Ops__".
 
-inline "cic:/CoRN/algebra/CRings/G.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/G.var" "CRing_Ops__".
 
 (* begin hide *)
 
-inline "cic:/CoRN/algebra/CRings/P.con".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__".
 
-inline "cic:/CoRN/algebra/CRings/Q.con".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__".
 
 (* end hide *)
 
 (* UNEXPORTED
-Section Part_Function_Mult.
+Section Part_Function_Mult
 *)
 
 inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
@@ -856,21 +912,21 @@ inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
 inline "cic:/CoRN/algebra/CRings/Fmult.con".
 
 (* UNEXPORTED
-End Part_Function_Mult.
+End Part_Function_Mult
 *)
 
 (* UNEXPORTED
-Section Part_Function_Nth_Power.
+Section Part_Function_Nth_Power
 *)
 
-inline "cic:/CoRN/algebra/CRings/n.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var" "CRing_Ops__Part_Function_Nth_Power__".
 
 inline "cic:/CoRN/algebra/CRings/part_function_nth_strext.con".
 
 inline "cic:/CoRN/algebra/CRings/Fnth.con".
 
 (* UNEXPORTED
-End Part_Function_Nth_Power.
+End Part_Function_Nth_Power
 *)
 
 (*#*
@@ -878,7 +934,7 @@ End Part_Function_Nth_Power.
 %\end{convention}%
 *)
 
-inline "cic:/CoRN/algebra/CRings/R'.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var" "CRing_Ops__".
 
 inline "cic:/CoRN/algebra/CRings/included_FMult.con".
 
@@ -886,14 +942,14 @@ inline "cic:/CoRN/algebra/CRings/included_FMult'.con".
 
 inline "cic:/CoRN/algebra/CRings/included_FMult''.con".
 
-inline "cic:/CoRN/algebra/CRings/n.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/n.var" "CRing_Ops__".
 
 inline "cic:/CoRN/algebra/CRings/included_FNth.con".
 
 inline "cic:/CoRN/algebra/CRings/included_FNth'.con".
 
 (* UNEXPORTED
-End CRing_Ops.
+End CRing_Ops
 *)
 
 inline "cic:/CoRN/algebra/CRings/Fscalmult.con".
@@ -902,36 +958,48 @@ inline "cic:/CoRN/algebra/CRings/Fscalmult.con".
 Implicit Arguments Fmult [R].
 *)
 
+(* NOTATION
+Infix "{*}" := Fmult (at level 40, left associativity).
+*)
+
 (* UNEXPORTED
 Implicit Arguments Fscalmult [R].
 *)
 
+(* NOTATION
+Infix "{**}" := Fscalmult (at level 40, left associativity).
+*)
+
 (* UNEXPORTED
 Implicit Arguments Fnth [R].
 *)
 
+(* NOTATION
+Infix "{^}" := Fnth (at level 30, right associativity).
+*)
+
 (* UNEXPORTED
-Section ScalarMultiplication.
+Section ScalarMultiplication
 *)
 
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var" "ScalarMultiplication__".
 
-inline "cic:/CoRN/algebra/CRings/F.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var" "ScalarMultiplication__".
 
 (* begin hide *)
 
-inline "cic:/CoRN/algebra/CRings/P.con".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__".
 
 (* end hide *)
 
-inline "cic:/CoRN/algebra/CRings/R'.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var" "ScalarMultiplication__".
 
 inline "cic:/CoRN/algebra/CRings/included_FScalMult.con".
 
 inline "cic:/CoRN/algebra/CRings/included_FScalMult'.con".
 
 (* UNEXPORTED
-End ScalarMultiplication.
+End ScalarMultiplication
 *)
 
 (* UNEXPORTED