set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_NthCoeff".
+include "CoRN.ma".
+
(* $Id: CPoly_NthCoeff.v,v 1.6 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CPolynomials
-*)
+include "algebra/CPolynomials.ma".
(*#*
* Polynomials: Nth Coefficient
*)
(* UNEXPORTED
-Section NthCoeff_def.
+Section NthCoeff_def
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var.
+alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var".
(* begin hide *)
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
(* end hide *)
(*#*
+ ... + an X^n#, the [Zero]-th coefficient is $a_0$#a0#, the first
is $a_1$#a1# etcetera. *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con".
(*#*
%\begin{shortcoming}%
%\end{shortcoming}%
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con".
(*#*
The following is probably NOT needed. These functions are
NOT extensional, that is, they are not CSetoid functions.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con".
(* The in_coeff predicate*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con".
(*#*
The [cpoly_zero] case should be [c [=] Zero] in order to be extensional.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con".
(* UNEXPORTED
-End NthCoeff_def.
+End NthCoeff_def
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section NthCoeff_props.
+Section NthCoeff_props
*)
(*#* ** Properties of [nth_coeff] *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var.
+alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var".
(* begin hide *)
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con".
(* UNEXPORTED
Hint Resolve nth_coeff_zero coeff_O_lin coeff_Sm_lin coeff_O_c_
coeff_O_x_mult coeff_Sm_x_mult coeff_Sm_mult_x_: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con".
(* UNEXPORTED
Hint Resolve nth_coeff_inv: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con".
(* UNEXPORTED
Hint Resolve nth_coeff_c_mult_p nth_coeff_p_mult_c_ nth_coeff_plus: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con".
(* UNEXPORTED
Hint Resolve nth_coeff_minus: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con".
(* UNEXPORTED
-End NthCoeff_props.
+End NthCoeff_props
*)
(* UNEXPORTED