set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields2".
-(* INCLUDE
-COrdFields
-*)
+include "CoRN.ma".
+
+include "algebra/COrdFields.ma".
(*#* printing one_div_succ %\ensuremath{\frac1{\cdot+1}}% *)
(*#**********************************)
(* UNEXPORTED
-Section Properties_of_leEq.
+Section Properties_of_leEq
*)
(*#**********************************)
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+alias id "R" = "cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var".
(* UNEXPORTED
-Section addition.
+Section addition
*)
(*#*
*** Addition and subtraction%\label{section:leEq-plus-minus}%
*)
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con".
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con".
(*#* Cancellation properties
*)
-inline cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con".
(*#* Laws for shifting
*)
-inline cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con".
(* UNEXPORTED
-End addition.
+End addition
*)
(* UNEXPORTED
-Section multiplication.
+Section multiplication
*)
(*#*
Multiplication and division respect [[<=]]
*)
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con".
-inline cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con".
(* UNEXPORTED
Hint Resolve recip_resp_leEq: algebra.
(*#* Cancellation properties
*)
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con".
(*#* Laws for shifting
*)
-inline cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con".
(* UNEXPORTED
Hint Resolve shift_leEq_div: algebra.
*)
-inline cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con.
+inline "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con".
(* UNEXPORTED
-End multiplication.
+End multiplication
*)
(* UNEXPORTED
-Section misc.
+Section misc
*)
(*#*
*** Miscellaneous Properties
*)
-inline cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/nring_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con.
+inline "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con".
-inline cic:/CoRN/algebra/COrdFields2/leEq_nring.con.
+inline "cic:/CoRN/algebra/COrdFields2/leEq_nring.con".
-inline cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con.
+inline "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/power_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con".
-inline cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con.
+inline "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con".
-inline cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/approach_zero.con.
+inline "cic:/CoRN/algebra/COrdFields2/approach_zero.con".
-inline cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con.
+inline "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con".
(* UNEXPORTED
-End misc.
+End misc
*)
-inline cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con".
(* UNEXPORTED
-End Properties_of_leEq.
+End Properties_of_leEq
*)
(*#**********************************)
(* UNEXPORTED
-Section PosP_properties.
+Section PosP_properties
*)
(*#**********************************)
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+alias id "R" = "cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var".
(* begin hide *)
+(* NOTATION
+Notation ZeroR := (Zero:R).
+*)
+
+(* NOTATION
+Notation OneR := (One:R).
+*)
+
(* end hide *)
-inline cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_square.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_square.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_wd.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_wd.con".
-inline cic:/CoRN/algebra/COrdFields2/even_power_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/even_power_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_nring_S.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con".
-inline cic:/CoRN/algebra/COrdFields2/square_eq_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/square_eq_neg.con.
+inline "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con".
(* UNEXPORTED
-End PosP_properties.
+End PosP_properties
*)
(* UNEXPORTED
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ.con".
(* UNEXPORTED
Implicit Arguments one_div_succ [R].
*)
(* UNEXPORTED
-Section One_div_succ_properties.
+Section One_div_succ_properties
*)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+alias id "R" = "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con".
(* UNEXPORTED
-End One_div_succ_properties.
+End One_div_succ_properties
*)
(*#*
** Properties of [Half]
*)
-inline cic:/CoRN/algebra/COrdFields2/Half.con.
+inline "cic:/CoRN/algebra/COrdFields2/Half.con".
(* UNEXPORTED
Implicit Arguments Half [R].
*)
(* UNEXPORTED
-Section Half_properties.
+Section Half_properties
*)
(*#*
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+alias id "R" = "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var".
-inline cic:/CoRN/algebra/COrdFields2/half_1.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_1.con".
(* UNEXPORTED
Hint Resolve half_1: algebra.
*)
-inline cic:/CoRN/algebra/COrdFields2/pos_half.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_half.con".
-inline cic:/CoRN/algebra/COrdFields2/half_1'.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_1'.con".
-inline cic:/CoRN/algebra/COrdFields2/half_2.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_2.con".
-inline cic:/CoRN/algebra/COrdFields2/half_lt1.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_lt1.con".
-inline cic:/CoRN/algebra/COrdFields2/half_3.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_3.con".
(* UNEXPORTED
-End Half_properties.
+End Half_properties
*)
(* UNEXPORTED