set "baseuri" "cic:/matita/CoRN-Decl/transc/Trigonometric".
+include "CoRN.ma".
+
(* $Id: Trigonometric.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-TaylorSeries
-*)
+include "transc/TaylorSeries.ma".
(*#* *The Trigonometric Functions
*)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* First, we need a lemma on mappings. *)
-inline cic:/CoRN/transc/Trigonometric/maps_translation.con.
+inline "cic:/CoRN/transc/Trigonometric/maps_translation.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section Sine_and_Cosine.
+Section Sine_and_Cosine
*)
(*#* Sine, cosine and tangent at [Zero]. *)
-inline cic:/CoRN/transc/Trigonometric/Sin_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_zero.con".
-inline cic:/CoRN/transc/Trigonometric/Cos_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Cos_zero.con".
(* UNEXPORTED
Hint Resolve Sin_zero Cos_zero: algebra.
Opaque Sine Cosine.
*)
-inline cic:/CoRN/transc/Trigonometric/Tan_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Tan_zero.con".
(* UNEXPORTED
Transparent Sine Cosine.
Continuity of sine and cosine are trivial.
*)
-inline cic:/CoRN/transc/Trigonometric/Continuous_Sin.con.
+inline "cic:/CoRN/transc/Trigonometric/Continuous_Sin.con".
-inline cic:/CoRN/transc/Trigonometric/Continuous_Cos.con.
+inline "cic:/CoRN/transc/Trigonometric/Continuous_Cos.con".
(*#*
The rules for the derivative of the sine and cosine function; we begin by proving that their defining sequences can be expressed in terms of one another.
*)
-inline cic:/CoRN/transc/Trigonometric/cos_sin_seq.con.
+inline "cic:/CoRN/transc/Trigonometric/cos_sin_seq.con".
-inline cic:/CoRN/transc/Trigonometric/sin_cos_seq.con.
+inline "cic:/CoRN/transc/Trigonometric/sin_cos_seq.con".
-inline cic:/CoRN/transc/Trigonometric/Derivative_Sin.con.
+inline "cic:/CoRN/transc/Trigonometric/Derivative_Sin.con".
-inline cic:/CoRN/transc/Trigonometric/Derivative_Cos.con.
+inline "cic:/CoRN/transc/Trigonometric/Derivative_Cos.con".
(* UNEXPORTED
Hint Resolve Derivative_Sin Derivative_Cos: derivate.
*)
(* UNEXPORTED
-Section Sine_of_Sum.
+Section Sine_of_Sum
*)
(*#*
(* begin hide *)
-inline cic:/CoRN/transc/Trigonometric/F.con.
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline cic:/CoRN/transc/Trigonometric/G.con.
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline cic:/CoRN/transc/Trigonometric/F'.con.
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F'.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline cic:/CoRN/transc/Trigonometric/G'.con.
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G'.con" "Sine_and_Cosine__Sine_of_Sum__".
(* end hide *)
Transparent FAbs.
*)
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con".
(* UNEXPORTED
Opaque FAbs.
Transparent FAbs.
*)
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con".
(* UNEXPORTED
-End Sine_of_Sum.
+End Sine_of_Sum
*)
(* UNEXPORTED
Opaque Sine Cosine.
*)
-inline cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con.
+inline "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con".
(* UNEXPORTED
-End Sine_and_Cosine.
+End Sine_and_Cosine
*)