- Added new output in standard C.

[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 4d23037a59a44ae5bae141e0c4d03a5be11f6c7c..2aa33c7d26bc1116b190291521fc33eb06606329 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma
@@ -16,6 +16,8 @@
 
 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings".
 
+include "CoRN.ma".
+
 (* $Id: CRings.v,v 1.8 2004/04/23 10:00:53 lcf Exp $ *)
 
 (*#* printing [*] %\ensuremath\times% #×# *)
@@ -52,9 +54,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings".
 
 (*#* printing FortyEight %\ensuremath{\mathbf{48}}% #48# *)
 
-(* INCLUDE
-CSums
-*)
+include "algebra/CSums.ma".
 
 (* UNEXPORTED
 Transparent sym_eq.
@@ -73,21 +73,27 @@ We actually define commutative rings with identity.
 ** Definition of the notion of Ring
 *)
 
-inline cic:/CoRN/algebra/CRings/distributive.con.
+inline "cic:/CoRN/algebra/CRings/distributive.con".
 
 (* UNEXPORTED
 Implicit Arguments distributive [S].
 *)
 
-inline cic:/CoRN/algebra/CRings/is_CRing.ind.
+inline "cic:/CoRN/algebra/CRings/is_CRing.ind".
+
+inline "cic:/CoRN/algebra/CRings/CRing.ind".
 
-inline cic:/CoRN/algebra/CRings/CRing.ind.
+coercion cic:/matita/CoRN-Decl/algebra/CRings/cr_crr.con 0 (* compounds *).
 
-inline cic:/CoRN/algebra/CRings/cr_plus.con.
+inline "cic:/CoRN/algebra/CRings/cr_plus.con".
 
-inline cic:/CoRN/algebra/CRings/cr_inv.con.
+inline "cic:/CoRN/algebra/CRings/cr_inv.con".
 
-inline cic:/CoRN/algebra/CRings/cr_minus.con.
+inline "cic:/CoRN/algebra/CRings/cr_minus.con".
+
+(* NOTATION
+Notation One := (cr_one _).
+*)
 
 (* End_SpecReals *)
 
@@ -104,8 +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
 *)
 
 (*#*
@@ -114,36 +124,36 @@ Section CRing_axioms.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/CRing_axioms/R.var".
 
-inline cic:/CoRN/algebra/CRings/CRing_is_CRing.con.
+inline "cic:/CoRN/algebra/CRings/CRing_is_CRing.con".
 
-inline cic:/CoRN/algebra/CRings/mult_assoc.con.
+inline "cic:/CoRN/algebra/CRings/mult_assoc.con".
 
-inline cic:/CoRN/algebra/CRings/mult_commutes.con.
+inline "cic:/CoRN/algebra/CRings/mult_commutes.con".
 
-inline cic:/CoRN/algebra/CRings/mult_mon.con.
+inline "cic:/CoRN/algebra/CRings/mult_mon.con".
 
 (* End_SpecReals *)
 
-inline cic:/CoRN/algebra/CRings/dist.con.
+inline "cic:/CoRN/algebra/CRings/dist.con".
 
-inline cic:/CoRN/algebra/CRings/ring_non_triv.con.
+inline "cic:/CoRN/algebra/CRings/ring_non_triv.con".
 
-inline cic:/CoRN/algebra/CRings/mult_wd.con.
+inline "cic:/CoRN/algebra/CRings/mult_wd.con".
 
-inline cic:/CoRN/algebra/CRings/mult_wdl.con.
+inline "cic:/CoRN/algebra/CRings/mult_wdl.con".
 
-inline cic:/CoRN/algebra/CRings/mult_wdr.con.
+inline "cic:/CoRN/algebra/CRings/mult_wdr.con".
 
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-End CRing_axioms.
+End CRing_axioms
 *)
 
 (* UNEXPORTED
-Section Ring_constructions.
+Section Ring_constructions
 *)
 
 (*#*
@@ -153,22 +163,22 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/Ring_constructions/R.var".
 
 (*#*
 The multiplicative monoid of a ring is defined as follows.
 *)
 
-inline cic:/CoRN/algebra/CRings/Build_multCMonoid.con.
+inline "cic:/CoRN/algebra/CRings/Build_multCMonoid.con".
 
 (* UNEXPORTED
-End Ring_constructions.
+End Ring_constructions
 *)
 
 (* End_SpecReals *)
 
 (* UNEXPORTED
-Section Ring_unfolded.
+Section Ring_unfolded
 *)
 
 (*#*
@@ -177,36 +187,36 @@ Section Ring_unfolded.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/algebra/CRings/mmR.con.
+inline "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__".
 
 (* end hide *)
 
-inline cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con".
 
-inline cic:/CoRN/algebra/CRings/mult_commut_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con".
 
 (* UNEXPORTED
 Hint Resolve mult_commut_unfolded: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/mult_one.con.
+inline "cic:/CoRN/algebra/CRings/mult_one.con".
 
-inline cic:/CoRN/algebra/CRings/one_mult.con.
+inline "cic:/CoRN/algebra/CRings/one_mult.con".
 
-inline cic:/CoRN/algebra/CRings/ring_dist_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con".
 
 (* UNEXPORTED
 Hint Resolve ring_dist_unfolded: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/ring_distl_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con".
 
 (* UNEXPORTED
-End Ring_unfolded.
+End Ring_unfolded
 *)
 
 (* UNEXPORTED
@@ -222,7 +232,7 @@ Hint Resolve ring_dist_unfolded ring_distl_unfolded: algebra.
 *)
 
 (* UNEXPORTED
-Section Ring_basics.
+Section Ring_basics
 *)
 
 (*#*
@@ -231,13 +241,13 @@ Section Ring_basics.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/Ring_basics/R.var".
 
-inline cic:/CoRN/algebra/CRings/one_ap_zero.con.
+inline "cic:/CoRN/algebra/CRings/one_ap_zero.con".
 
-inline cic:/CoRN/algebra/CRings/is_zero_rht.con.
+inline "cic:/CoRN/algebra/CRings/is_zero_rht.con".
 
-inline cic:/CoRN/algebra/CRings/is_zero_lft.con.
+inline "cic:/CoRN/algebra/CRings/is_zero_lft.con".
 
 (* UNEXPORTED
 Implicit Arguments is_zero_rht [S].
@@ -247,52 +257,52 @@ Implicit Arguments is_zero_rht [S].
 Implicit Arguments is_zero_lft [S].
 *)
 
-inline cic:/CoRN/algebra/CRings/cring_mult_zero.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_zero.con".
 
 (* UNEXPORTED
 Hint Resolve cring_mult_zero: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/x_mult_zero.con.
+inline "cic:/CoRN/algebra/CRings/x_mult_zero.con".
 
-inline cic:/CoRN/algebra/CRings/cring_mult_zero_op.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con".
 
 (* UNEXPORTED
 Hint Resolve cring_mult_zero_op: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con.
+inline "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con".
 
 (* UNEXPORTED
 Hint Resolve cring_inv_mult_lft: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con.
+inline "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con".
 
 (* UNEXPORTED
 Hint Resolve cring_inv_mult_rht: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con".
 
-inline cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con".
 
-inline cic:/CoRN/algebra/CRings/inv_mult_invol.con.
+inline "cic:/CoRN/algebra/CRings/inv_mult_invol.con".
 
-inline cic:/CoRN/algebra/CRings/ring_dist_minus.con.
+inline "cic:/CoRN/algebra/CRings/ring_dist_minus.con".
 
 (* UNEXPORTED
 Hint Resolve ring_dist_minus: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/ring_distl_minus.con.
+inline "cic:/CoRN/algebra/CRings/ring_distl_minus.con".
 
 (* UNEXPORTED
 Hint Resolve ring_distl_minus: algebra.
 *)
 
 (* UNEXPORTED
-End Ring_basics.
+End Ring_basics
 *)
 
 (* UNEXPORTED
@@ -324,7 +334,7 @@ especially geared towards CReals.
 *)
 
 (* UNEXPORTED
-Section exponentiation.
+Section exponentiation
 *)
 
 (*#*
@@ -334,26 +344,30 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/exponentiation/R.var".
 
 (* End_SpecReals *)
 
-inline cic:/CoRN/algebra/CRings/nexp.con.
+inline "cic:/CoRN/algebra/CRings/nexp.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_well_def.con.
+inline "cic:/CoRN/algebra/CRings/nexp_well_def.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_strong_ext.con.
+inline "cic:/CoRN/algebra/CRings/nexp_strong_ext.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_op.con.
+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].
 *)
@@ -361,7 +375,7 @@ Implicit Arguments nexp_op [R].
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-Section nat_injection.
+Section nat_injection
 *)
 
 (*#*
@@ -370,7 +384,7 @@ Section nat_injection.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/nat_injection/R.var".
 
 (*#*
 The injection of Coq natural numbers into a ring is called [nring].
@@ -378,20 +392,20 @@ Note that this need not really be an injection; when it is, the ring is said
 to have characteristic [0].
 *)
 
-inline cic:/CoRN/algebra/CRings/nring.con.
+inline "cic:/CoRN/algebra/CRings/nring.con".
 
-inline cic:/CoRN/algebra/CRings/Char0.con.
+inline "cic:/CoRN/algebra/CRings/Char0.con".
 
 (* End_SpecReals *)
 
-inline cic:/CoRN/algebra/CRings/nring_comm_plus.con.
+inline "cic:/CoRN/algebra/CRings/nring_comm_plus.con".
 
-inline cic:/CoRN/algebra/CRings/nring_comm_mult.con.
+inline "cic:/CoRN/algebra/CRings/nring_comm_mult.con".
 
 (* Begin_SpecReals *)
 
 (* UNEXPORTED
-End nat_injection.
+End nat_injection
 *)
 
 (* End_SpecReals *)
@@ -408,9 +422,53 @@ Implicit Arguments nring [R].
 
 (* End_SpecReals *)
 
-inline cic:/CoRN/algebra/CRings/one_plus_one.con.
+(* NOTATION
+Notation Two := (nring 2).
+*)
 
-inline cic:/CoRN/algebra/CRings/x_plus_x.con.
+(* 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".
 
 (* UNEXPORTED
 Hint Resolve one_plus_one x_plus_x: algebra.
@@ -420,10 +478,10 @@ Hint Resolve one_plus_one x_plus_x: algebra.
 In a ring of characteristic zero, [nring] is really an injection.
 *)
 
-inline cic:/CoRN/algebra/CRings/nring_different.con.
+inline "cic:/CoRN/algebra/CRings/nring_different.con".
 
 (* UNEXPORTED
-Section int_injection.
+Section int_injection
 *)
 
 (*#*
@@ -433,7 +491,7 @@ Let [R] be a ring.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/int_injection/R.var".
 
 (*#*
 The injection of Coq integers into a ring is called [zring]. Again,
@@ -443,27 +501,27 @@ The first definition is now obsolete, having been replaced by a more efficient
 one. It is kept to avoid having to redo all the proofs.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old.con.
+inline "cic:/CoRN/algebra/CRings/zring_old.con".
 
-inline cic:/CoRN/algebra/CRings/zring_old_zero.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_zero.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_zero: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_diff.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_diff.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_diff.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_plus_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_plus_nat: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_inv_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_inv_nat: algebra.
@@ -473,97 +531,97 @@ Hint Resolve zring_old_inv_nat: algebra.
 Hint Resolve zring_old_diff: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_plus.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_plus.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_plus: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_inv.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_inv: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_minus.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_minus.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_minus: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_mult.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_mult.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_mult: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_one.con".
 
 (* UNEXPORTED
 Hint Resolve zring_old_one: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_old_inv_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv_one.con".
 
 (*#************** new def of zring. ***********************)
 
 (*#* The [zring] function can be defined directly.  This is done here.
 *)
 
-inline cic:/CoRN/algebra/CRings/pring_aux.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux.con".
 
-inline cic:/CoRN/algebra/CRings/pring.con.
+inline "cic:/CoRN/algebra/CRings/pring.con".
 
-inline cic:/CoRN/algebra/CRings/zring.con.
+inline "cic:/CoRN/algebra/CRings/zring.con".
 
-inline cic:/CoRN/algebra/CRings/pring_aux_lemma.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux_lemma.con".
 
-inline cic:/CoRN/algebra/CRings/double_nring.con.
+inline "cic:/CoRN/algebra/CRings/double_nring.con".
 
 (* UNEXPORTED
 Hint Resolve pring_aux_lemma double_nring: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/pring_aux_nring.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux_nring.con".
 
 (* UNEXPORTED
 Hint Resolve pring_aux_nring: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/pring_convert.con.
+inline "cic:/CoRN/algebra/CRings/pring_convert.con".
 
 (* UNEXPORTED
 Hint Resolve pring_convert: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_zring_old.con.
+inline "cic:/CoRN/algebra/CRings/zring_zring_old.con".
 
 (* UNEXPORTED
 Hint Resolve zring_zring_old: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zring_zero.con.
+inline "cic:/CoRN/algebra/CRings/zring_zero.con".
 
-inline cic:/CoRN/algebra/CRings/zring_diff.con.
+inline "cic:/CoRN/algebra/CRings/zring_diff.con".
 
-inline cic:/CoRN/algebra/CRings/zring_plus_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_plus_nat.con".
 
-inline cic:/CoRN/algebra/CRings/zring_inv_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv_nat.con".
 
-inline cic:/CoRN/algebra/CRings/zring_plus.con.
+inline "cic:/CoRN/algebra/CRings/zring_plus.con".
 
-inline cic:/CoRN/algebra/CRings/zring_inv.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv.con".
 
-inline cic:/CoRN/algebra/CRings/zring_minus.con.
+inline "cic:/CoRN/algebra/CRings/zring_minus.con".
 
-inline cic:/CoRN/algebra/CRings/zring_mult.con.
+inline "cic:/CoRN/algebra/CRings/zring_mult.con".
 
-inline cic:/CoRN/algebra/CRings/zring_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_one.con".
 
-inline cic:/CoRN/algebra/CRings/zring_inv_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv_one.con".
 
 (* UNEXPORTED
-End int_injection.
+End int_injection
 *)
 
 (* UNEXPORTED
@@ -577,7 +635,7 @@ Hint Resolve pring_convert zring_zero zring_diff zring_plus_nat zring_inv_nat
 *)
 
 (* UNEXPORTED
-Section Ring_sums.
+Section Ring_sums
 *)
 
 (*#*
@@ -586,56 +644,56 @@ Section Ring_sums.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/Ring_sums/R.var".
 
 (*#*
 *** Infinite Ring sums
 *)
 
 (* UNEXPORTED
-Section infinite_ring_sums.
+Section infinite_ring_sums
 *)
 
-inline cic:/CoRN/algebra/CRings/Sum_upto.con.
+inline "cic:/CoRN/algebra/CRings/Sum_upto.con".
 
-inline cic:/CoRN/algebra/CRings/sum_upto_O.con.
+inline "cic:/CoRN/algebra/CRings/sum_upto_O.con".
 
-inline cic:/CoRN/algebra/CRings/Sum_from_upto.con.
+inline "cic:/CoRN/algebra/CRings/Sum_from_upto.con".
 
 (*#*
 Here's an alternative def of [Sum_from_upto], with a lemma that
 it's equivalent to the original.
 *)
 
-inline cic:/CoRN/algebra/CRings/seq_from.con.
+inline "cic:/CoRN/algebra/CRings/seq_from.con".
 
-inline cic:/CoRN/algebra/CRings/Sum_from_upto_alt.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
 *)
 
-inline cic:/CoRN/algebra/CRings/RList_Mem.con.
+inline "cic:/CoRN/algebra/CRings/RList_Mem.con".
 
-inline cic:/CoRN/algebra/CRings/List_Sum_upto.con.
+inline "cic:/CoRN/algebra/CRings/List_Sum_upto.con".
 
-inline cic:/CoRN/algebra/CRings/list_sum_upto_O.con.
+inline "cic:/CoRN/algebra/CRings/list_sum_upto_O.con".
 
-inline cic:/CoRN/algebra/CRings/List_Sum_from_upto.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
 *)
 
 (*#*
@@ -646,47 +704,47 @@ Let [R] be a ring.
 *)
 
 (* UNEXPORTED
-Section Dist_properties.
+Section Dist_properties
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/Dist_properties/R.var".
 
-inline cic:/CoRN/algebra/CRings/dist_1b.con.
+inline "cic:/CoRN/algebra/CRings/dist_1b.con".
 
 (* UNEXPORTED
 Hint Resolve dist_1b: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/dist_2a.con.
+inline "cic:/CoRN/algebra/CRings/dist_2a.con".
 
 (* UNEXPORTED
 Hint Resolve dist_2a: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/dist_2b.con.
+inline "cic:/CoRN/algebra/CRings/dist_2b.con".
 
 (* UNEXPORTED
 Hint Resolve dist_2b: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con".
 
 (* UNEXPORTED
 Hint Resolve mult_distr_sum0_lft.
 *)
 
-inline cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con".
 
 (* UNEXPORTED
 Hint Resolve mult_distr_sum_lft: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con".
 
-inline cic:/CoRN/algebra/CRings/sumx_const.con.
+inline "cic:/CoRN/algebra/CRings/sumx_const.con".
 
 (* UNEXPORTED
-End Dist_properties.
+End Dist_properties
 *)
 
 (* UNEXPORTED
@@ -702,111 +760,111 @@ Let [R] be a ring.
 *)
 
 (* UNEXPORTED
-Section NExp_properties.
+Section NExp_properties
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/NExp_properties/R.var".
 
-inline cic:/CoRN/algebra/CRings/nexp_wd.con.
+inline "cic:/CoRN/algebra/CRings/nexp_wd.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_strext.con.
+inline "cic:/CoRN/algebra/CRings/nexp_strext.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_Sn.con.
+inline "cic:/CoRN/algebra/CRings/nexp_Sn.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_wd nexp_Sn: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/nexp_plus.con.
+inline "cic:/CoRN/algebra/CRings/nexp_plus.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_plus: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/one_nexp.con.
+inline "cic:/CoRN/algebra/CRings/one_nexp.con".
 
 (* UNEXPORTED
 Hint Resolve one_nexp: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/mult_nexp.con.
+inline "cic:/CoRN/algebra/CRings/mult_nexp.con".
 
 (* UNEXPORTED
 Hint Resolve mult_nexp: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/nexp_mult.con.
+inline "cic:/CoRN/algebra/CRings/nexp_mult.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_mult: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/zero_nexp.con.
+inline "cic:/CoRN/algebra/CRings/zero_nexp.con".
 
 (* UNEXPORTED
 Hint Resolve zero_nexp: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/inv_nexp_even.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_even.con".
 
 (* UNEXPORTED
 Hint Resolve inv_nexp_even: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/inv_nexp_two.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_two.con".
 
 (* UNEXPORTED
 Hint Resolve inv_nexp_two: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/inv_nexp_odd.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_odd.con".
 
 (* UNEXPORTED
 Hint Resolve inv_nexp_odd: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/nexp_one.con.
+inline "cic:/CoRN/algebra/CRings/nexp_one.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_one: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/nexp_two.con.
+inline "cic:/CoRN/algebra/CRings/nexp_two.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_two: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/inv_one_even_nexp.con.
+inline "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con".
 
 (* UNEXPORTED
 Hint Resolve inv_one_even_nexp: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con.
+inline "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con".
 
 (* UNEXPORTED
 Hint Resolve inv_one_odd_nexp: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/square_plus.con.
+inline "cic:/CoRN/algebra/CRings/square_plus.con".
 
-inline cic:/CoRN/algebra/CRings/square_minus.con.
+inline "cic:/CoRN/algebra/CRings/square_minus.con".
 
-inline cic:/CoRN/algebra/CRings/nexp_funny.con.
+inline "cic:/CoRN/algebra/CRings/nexp_funny.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_funny: algebra.
 *)
 
-inline cic:/CoRN/algebra/CRings/nexp_funny'.con.
+inline "cic:/CoRN/algebra/CRings/nexp_funny'.con".
 
 (* UNEXPORTED
 Hint Resolve nexp_funny': algebra.
 *)
 
 (* UNEXPORTED
-End NExp_properties.
+End NExp_properties
 *)
 
 (* UNEXPORTED
@@ -817,7 +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
 *)
 
 (*#*
@@ -831,44 +889,44 @@ respectively [P] and [Q].
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R.var.
+alias id "R" = "cic:/CoRN/algebra/CRings/CRing_Ops/R.var".
 
-inline cic:/CoRN/algebra/CRings/F.var.
+alias id "F" = "cic:/CoRN/algebra/CRings/CRing_Ops/F.var".
 
-inline cic:/CoRN/algebra/CRings/G.var.
+alias id "G" = "cic:/CoRN/algebra/CRings/CRing_Ops/G.var".
 
 (* 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.
+inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
 
-inline cic:/CoRN/algebra/CRings/Fmult.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.
+alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var".
 
-inline cic:/CoRN/algebra/CRings/part_function_nth_strext.con.
+inline "cic:/CoRN/algebra/CRings/part_function_nth_strext.con".
 
-inline cic:/CoRN/algebra/CRings/Fnth.con.
+inline "cic:/CoRN/algebra/CRings/Fnth.con".
 
 (* UNEXPORTED
-End Part_Function_Nth_Power.
+End Part_Function_Nth_Power
 *)
 
 (*#*
@@ -876,60 +934,72 @@ End Part_Function_Nth_Power.
 %\end{convention}%
 *)
 
-inline cic:/CoRN/algebra/CRings/R'.var.
+alias id "R'" = "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var".
 
-inline cic:/CoRN/algebra/CRings/included_FMult.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult.con".
 
-inline cic:/CoRN/algebra/CRings/included_FMult'.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult'.con".
 
-inline cic:/CoRN/algebra/CRings/included_FMult''.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult''.con".
 
-inline cic:/CoRN/algebra/CRings/n.var.
+alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/n.var".
 
-inline cic:/CoRN/algebra/CRings/included_FNth.con.
+inline "cic:/CoRN/algebra/CRings/included_FNth.con".
 
-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.
+inline "cic:/CoRN/algebra/CRings/Fscalmult.con".
 
 (* UNEXPORTED
 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.
+alias id "R" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var".
 
-inline cic:/CoRN/algebra/CRings/F.var.
+alias id "F" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var".
 
 (* 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.
+alias id "R'" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var".
 
-inline cic:/CoRN/algebra/CRings/included_FScalMult.con.
+inline "cic:/CoRN/algebra/CRings/included_FScalMult.con".
 
-inline cic:/CoRN/algebra/CRings/included_FScalMult'.con.
+inline "cic:/CoRN/algebra/CRings/included_FScalMult'.con".
 
 (* UNEXPORTED
-End ScalarMultiplication.
+End ScalarMultiplication
 *)
 
 (* UNEXPORTED