set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields".
+include "CoRN.ma".
+
(* $Id: COrdFields.v,v 1.6 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [<] %\ensuremath<% #<# *)
(*#* printing FortyEightNZ %\ensuremath{\mathbf{48}}% #48# *)
-(* INCLUDE
-FieldReflection
-*)
+include "tactics/FieldReflection.ma".
(* ORDERED FIELDS *)
(* Begin_SpecReals *)
-inline cic:/CoRN/algebra/COrdFields/strictorder.ind.
+inline "cic:/CoRN/algebra/COrdFields/strictorder.ind".
(* UNEXPORTED
Implicit Arguments strictorder [A].
Implicit Arguments so_asym [A R].
*)
-inline cic:/CoRN/algebra/COrdFields/is_COrdField.ind.
+inline "cic:/CoRN/algebra/COrdFields/is_COrdField.ind".
+
+inline "cic:/CoRN/algebra/COrdFields/COrdField.ind".
-inline cic:/CoRN/algebra/COrdFields/COrdField.ind.
+coercion cic:/matita/CoRN-Decl/algebra/COrdFields/cof_crr.con 0 (* compounds *).
(*#*
%\begin{nameconvention}%
Implicit Arguments cof_less [c].
*)
-inline cic:/CoRN/algebra/COrdFields/greater.con.
+(* NOTATION
+Infix "[<]" := cof_less (at level 70, no associativity).
+*)
+
+inline "cic:/CoRN/algebra/COrdFields/greater.con".
(* UNEXPORTED
Implicit Arguments greater [F].
*)
+(* NOTATION
+Infix "[>]" := greater (at level 70, no associativity).
+*)
+
(* End_SpecReals *)
(*#*
Less or equal is defined as ``not greater than''.
*)
-inline cic:/CoRN/algebra/COrdFields/leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq.con".
(*#*
%\begin{nameconvention}%
Implicit Arguments leEq [F].
*)
+(* NOTATION
+Infix "[<=]" := leEq (at level 70, no associativity).
+*)
+
(* UNEXPORTED
Section COrdField_axioms.
*)
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields/F.var.
+inline "cic:/CoRN/algebra/COrdFields/F.var".
-inline cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con.
+inline "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con".
-inline cic:/CoRN/algebra/COrdFields/less_strorder.con.
+inline "cic:/CoRN/algebra/COrdFields/less_strorder.con".
-inline cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/less_irreflexive.con.
+inline "cic:/CoRN/algebra/COrdFields/less_irreflexive.con".
-inline cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/less_conf_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/less_conf_ap.con".
-inline cic:/CoRN/algebra/COrdFields/less_wdr.con.
+inline "cic:/CoRN/algebra/COrdFields/less_wdr.con".
-inline cic:/CoRN/algebra/COrdFields/less_wdl.con.
+inline "cic:/CoRN/algebra/COrdFields/less_wdl.con".
(* UNEXPORTED
End COrdField_axioms.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/less_imp_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/less_imp_ap.con".
-inline cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con".
-inline cic:/CoRN/algebra/COrdFields/ap_imp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/ap_imp_less.con".
(*#*
Now properties which can be derived.
*)
-inline cic:/CoRN/algebra/COrdFields/less_cotransitive.con.
+inline "cic:/CoRN/algebra/COrdFields/less_cotransitive.con".
-inline cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/pos_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con".
(* Main characterization of less *)
-inline cic:/CoRN/algebra/COrdFields/leEq_not_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con".
(* UNEXPORTED
End OrdField_basics.
(*#* ** Basic properties of [ [<=] ]
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/leEq_wdr.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_wdr.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_wdl.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_wdl.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_reflexive.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con".
(* UNEXPORTED
Declare Left Step leEq_wdl.
Declare Right Step leEq_wdr.
*)
-inline cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con".
-inline cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con".
-inline cic:/CoRN/algebra/COrdFields/less_leEq_trans.con.
+inline "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_less_trans.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_transitive.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_transitive.con".
-inline cic:/CoRN/algebra/COrdFields/less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/less_leEq.con".
(* UNEXPORTED
End Basic_Properties_of_leEq.
e.g.%\% [x[/]TwoNZ].
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/pos_one.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_one.con".
-inline cic:/CoRN/algebra/COrdFields/nring_less_succ.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_less_succ.con".
-inline cic:/CoRN/algebra/COrdFields/nring_less.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_less.con".
-inline cic:/CoRN/algebra/COrdFields/nring_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_leEq.con".
-inline cic:/CoRN/algebra/COrdFields/nring_apart.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_apart.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con".
-inline cic:/CoRN/algebra/COrdFields/Snring.con.
+inline "cic:/CoRN/algebra/COrdFields/Snring.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields/pos_Snring.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_Snring.con".
-inline cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
(* UNEXPORTED
Section up_to_four.
%\end{nameconvention}%
*)
-inline cic:/CoRN/algebra/COrdFields/less_plusOne.con.
+inline "cic:/CoRN/algebra/COrdFields/less_plusOne.con".
-inline cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con.
+inline "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con".
-inline cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_two.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_two.con".
-inline cic:/CoRN/algebra/COrdFields/two_less_three.con.
+inline "cic:/CoRN/algebra/COrdFields/two_less_three.con".
-inline cic:/CoRN/algebra/COrdFields/three_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/three_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_two.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_two.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_three.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_three.con".
-inline cic:/CoRN/algebra/COrdFields/two_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/two_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_three.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_three.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_four.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_four.con".
-inline cic:/CoRN/algebra/COrdFields/two_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/two_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/three_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/three_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/four_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/four_ap_zero.con".
(* UNEXPORTED
End up_to_four.
(*#* *** Properties of some other numbers *)
-inline cic:/CoRN/algebra/COrdFields/pos_six.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_six.con".
-inline cic:/CoRN/algebra/COrdFields/pos_eight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_eight.con".
-inline cic:/CoRN/algebra/COrdFields/pos_nine.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_nine.con".
-inline cic:/CoRN/algebra/COrdFields/pos_twelve.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_twelve.con".
-inline cic:/CoRN/algebra/COrdFields/pos_sixteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_sixteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_eighteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_eighteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_twentyfour.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con".
-inline cic:/CoRN/algebra/COrdFields/pos_fortyeight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con".
-inline cic:/CoRN/algebra/COrdFields/six_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/six_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/eight_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nine_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con".
(* UNEXPORTED
End More_than_four.
Declare Right Step leEq_wdr.
*)
+(* NOTATION
+Notation " x [/]OneNZ" := (x[/] One[//]ring_non_triv _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwoNZ" := (x[/] Two[//]two_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]ThreeNZ" := (x[/] Three[//]three_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]FourNZ" := (x[/] Four[//]four_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]SixNZ" := (x[/] Six[//]six_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]EightNZ" := (x[/] Eight[//]eight_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]NineNZ" := (x[/] Nine[//]nine_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwelveNZ" := (x[/] Twelve[//]twelve_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]SixteenNZ" := (x[/] Sixteen[//]sixteen_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]EighteenNZ" := (x[/] Eighteen[//]eighteen_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]TwentyFourNZ" := (x[/] TwentyFour[//]twentyfour_ap_zero _) (at level 20).
+*)
+
+(* NOTATION
+Notation " x [/]FortyEightNZ" := (x[/] FortyEight[//]fortyeight_ap_zero _) (at level 20).
+*)
+
(* UNEXPORTED
Section consequences_of_infinity.
*)
*** Consequences of infinity
*)
-inline cic:/CoRN/algebra/COrdFields/F.var.
+inline "cic:/CoRN/algebra/COrdFields/F.var".
-inline cic:/CoRN/algebra/COrdFields/square_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/square_eq.con".
(*#*
Ordered fields have characteristic zero.
*)
-inline cic:/CoRN/algebra/COrdFields/char0_OrdField.con.
+inline "cic:/CoRN/algebra/COrdFields/char0_OrdField.con".
(* UNEXPORTED
End consequences_of_infinity.
** Properties of [[<]]
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
(*#*
We do not use a special predicate for positivity,
*)
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con".
-inline cic:/CoRN/algebra/COrdFields/inv_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/inv_resp_less.con".
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields/minus_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/minus_resp_less.con".
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con".
(*#*
For versions of [plus_resp_less_both] where one [ [<] ] in the
Cancellation laws
*)
-inline cic:/CoRN/algebra/COrdFields/plus_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con".
-inline cic:/CoRN/algebra/COrdFields/inv_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con".
(*#*
Coq%(see the Coq shortcoming in Section~\ref{section:setoid-basics})%.
*)
-inline cic:/CoRN/algebra/COrdFields/shift_less_plus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_plus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_plus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_minus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_minus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_plus_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_plus_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_plus_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_minus_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_minus_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_minus_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con".
(*#*
Some special cases of laws for shifting.
*)
-inline cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con".
-inline cic:/CoRN/algebra/COrdFields/qltone.con.
+inline "cic:/CoRN/algebra/COrdFields/qltone.con".
(* UNEXPORTED
End addition.
*)
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/recip_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con".
-inline cic:/CoRN/algebra/COrdFields/recip_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/recip_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_less.con".
(*#* Cancellation laws
*)
-inline cic:/CoRN/algebra/COrdFields/mult_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con".
(*#*
Laws for shifting
on plus and minus.%
*)
-inline cic:/CoRN/algebra/COrdFields/shift_div_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_div_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_div_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_div_less'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_div.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_div.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_mult.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_mult.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_mult'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_mult_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_mult_less.con".
(*#* Other properties of multiplication and division
*)
-inline cic:/CoRN/algebra/COrdFields/minusOne_less.con.
+inline "cic:/CoRN/algebra/COrdFields/minusOne_less.con".
-inline cic:/CoRN/algebra/COrdFields/swap_div.con.
+inline "cic:/CoRN/algebra/COrdFields/swap_div.con".
-inline cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con.
+inline "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_two.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_two.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_two'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_two'.con".
(*
Apply mult_cancel_less with (Two::R).
Qed.
*)
-inline cic:/CoRN/algebra/COrdFields/pos_div_three.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_three.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_three'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_three'.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_four.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_four'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_four'.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_six.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_six.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_eight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_eight.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_nine.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_nine.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_twelve.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con".
(* UNEXPORTED
End multiplication.
*** Miscellaneous properties
*)
-inline cic:/CoRN/algebra/COrdFields/nring_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_pos.con".
-inline cic:/CoRN/algebra/COrdFields/less_nring.con.
+inline "cic:/CoRN/algebra/COrdFields/less_nring.con".
-inline cic:/CoRN/algebra/COrdFields/pos_nring_fac.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con".
-inline cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con.
+inline "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con".
-inline cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con.
+inline "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con".
-inline cic:/CoRN/algebra/COrdFields/Sum_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/positive_Sum_two.con.
+inline "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con".
-inline cic:/CoRN/algebra/COrdFields/positive_Sumx.con.
+inline "cic:/CoRN/algebra/COrdFields/positive_Sumx.con".
-inline cic:/CoRN/algebra/COrdFields/negative_Sumx.con.
+inline "cic:/CoRN/algebra/COrdFields/negative_Sumx.con".
(* UNEXPORTED
End misc.