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% #×# *)
(*#* printing FortyEight %\ensuremath{\mathbf{48}}% #48# *)
-(* INCLUDE
-CSums
-*)
+include "algebra/CSums.ma".
(* UNEXPORTED
Transparent sym_eq.
** 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 *)
Implicit Arguments cr_mult [c].
*)
+(* NOTATION
+Infix "[*]" := cr_mult (at level 40, left associativity).
+*)
+
(* UNEXPORTED
-Section CRing_axioms.
+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
*)
(*#*
%\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
*)
(*#*
%\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
*)
(* UNEXPORTED
-Section Ring_basics.
+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].
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
*)
(* UNEXPORTED
-Section exponentiation.
+Section exponentiation
*)
(*#*
%\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].
*)
(* Begin_SpecReals *)
(* UNEXPORTED
-Section nat_injection.
+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].
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 *)
(* 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.
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
*)
(*#*
%\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,
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.
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
*)
(* UNEXPORTED
-Section Ring_sums.
+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
*)
(*#*
*)
(* 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
*)
(* 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
*)
(* UNEXPORTED
-Section CRing_Ops.
+Section CRing_Ops
*)
(*#*
%\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
*)
(*#*
%\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