set "baseuri" "cic:/matita/CoRN-Decl/transc/SinCos".
+include "CoRN_notation.ma".
+
(* $Id: SinCos.v,v 1.6 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-Trigonometric
-*)
+include "transc/Trigonometric.ma".
(* UNEXPORTED
Section Sum_and_so_on.
(* begin hide *)
-inline cic:/CoRN/transc/SinCos/F.con.
+inline "cic:/CoRN/transc/SinCos/F.con".
-inline cic:/CoRN/transc/SinCos/G.con.
+inline "cic:/CoRN/transc/SinCos/G.con".
-inline cic:/CoRN/transc/SinCos/F'.con.
+inline "cic:/CoRN/transc/SinCos/F'.con".
-inline cic:/CoRN/transc/SinCos/G'.con.
+inline "cic:/CoRN/transc/SinCos/G'.con".
(* end hide *)
-inline cic:/CoRN/transc/SinCos/Sin_plus.con.
+inline "cic:/CoRN/transc/SinCos/Sin_plus.con".
-inline cic:/CoRN/transc/SinCos/Cos_plus.con.
+inline "cic:/CoRN/transc/SinCos/Cos_plus.con".
(* UNEXPORTED
Opaque Sine Cosine.
(*#* As a corollary we get the rule for the tangent of the sum. *)
-inline cic:/CoRN/transc/SinCos/Tan_plus.con.
+inline "cic:/CoRN/transc/SinCos/Tan_plus.con".
(* UNEXPORTED
Transparent Sine Cosine.
(*#* Sine, cosine and tangent of [[--]x]. *)
-inline cic:/CoRN/transc/SinCos/Cos_inv.con.
+inline "cic:/CoRN/transc/SinCos/Cos_inv.con".
-inline cic:/CoRN/transc/SinCos/Sin_inv.con.
+inline "cic:/CoRN/transc/SinCos/Sin_inv.con".
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve Cos_inv Sin_inv: algebra.
*)
-inline cic:/CoRN/transc/SinCos/Tan_inv.con.
+inline "cic:/CoRN/transc/SinCos/Tan_inv.con".
(* UNEXPORTED
Transparent Sine Cosine.
Hint Resolve Cos_zero: algebra.
*)
-inline cic:/CoRN/transc/SinCos/FFT.con.
+inline "cic:/CoRN/transc/SinCos/FFT.con".
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve FFT: algebra.
*)
-inline cic:/CoRN/transc/SinCos/FFT'.con.
+inline "cic:/CoRN/transc/SinCos/FFT'.con".
(* UNEXPORTED
End Sum_and_so_on.
Sine, cosine and tangent are strongly extensional and well defined.
*)
-inline cic:/CoRN/transc/SinCos/Sin_strext.con.
+inline "cic:/CoRN/transc/SinCos/Sin_strext.con".
-inline cic:/CoRN/transc/SinCos/Cos_strext.con.
+inline "cic:/CoRN/transc/SinCos/Cos_strext.con".
-inline cic:/CoRN/transc/SinCos/Tan_strext.con.
+inline "cic:/CoRN/transc/SinCos/Tan_strext.con".
-inline cic:/CoRN/transc/SinCos/Sin_wd.con.
+inline "cic:/CoRN/transc/SinCos/Sin_wd.con".
-inline cic:/CoRN/transc/SinCos/Cos_wd.con.
+inline "cic:/CoRN/transc/SinCos/Cos_wd.con".
-inline cic:/CoRN/transc/SinCos/Tan_wd.con.
+inline "cic:/CoRN/transc/SinCos/Tan_wd.con".
(*#*
The sine and cosine produce values in [[-1,1]].
*)
-inline cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/Sin_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/Sin_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/Cos_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/Cos_leEq_One.con".
(*#*
If the cosine is positive then the sine is in [(-1,1)].
*)
-inline cic:/CoRN/transc/SinCos/Sin_less_One.con.
+inline "cic:/CoRN/transc/SinCos/Sin_less_One.con".
-inline cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con".
(* UNEXPORTED
End Basic_Properties.