set "baseuri" "cic:/matita/CoRN-Decl/transc/RealPowers".
+include "CoRN.ma".
+
(* $Id: RealPowers.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
(*#* printing [!] %\ensuremath{\hat{\ }}% #^# *)
(*#* printing {!} %\ensuremath{\hat{\ }}% #^# *)
-(* INCLUDE
-Exponential
-*)
+include "transc/Exponential.ma".
(* UNEXPORTED
Opaque Expon.
[x [>] 0], inspired by the rules for manipulating these expressions.
*)
-inline cic:/CoRN/transc/RealPowers/power.con.
+inline "cic:/CoRN/transc/RealPowers/power.con".
+
+(* NOTATION
+Notation "x [!] y [//] Hy" := (power x y Hy) (at level 20).
+*)
(*#*
This definition yields a well defined, strongly extensional function
coincides with the exponential function.
*)
-inline cic:/CoRN/transc/RealPowers/power_wd.con.
+inline "cic:/CoRN/transc/RealPowers/power_wd.con".
-inline cic:/CoRN/transc/RealPowers/power_strext.con.
+inline "cic:/CoRN/transc/RealPowers/power_strext.con".
-inline cic:/CoRN/transc/RealPowers/power_plus.con.
+inline "cic:/CoRN/transc/RealPowers/power_plus.con".
-inline cic:/CoRN/transc/RealPowers/power_inv.con.
+inline "cic:/CoRN/transc/RealPowers/power_inv.con".
(* UNEXPORTED
Hint Resolve power_wd power_plus power_inv: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_minus.con.
+inline "cic:/CoRN/transc/RealPowers/power_minus.con".
-inline cic:/CoRN/transc/RealPowers/power_nat.con.
+inline "cic:/CoRN/transc/RealPowers/power_nat.con".
(* UNEXPORTED
Hint Resolve power_minus power_nat: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_zero.con.
+inline "cic:/CoRN/transc/RealPowers/power_zero.con".
-inline cic:/CoRN/transc/RealPowers/power_one.con.
+inline "cic:/CoRN/transc/RealPowers/power_one.con".
(* UNEXPORTED
Hint Resolve power_zero power_one: algebra.
Opaque nexp_op.
*)
-inline cic:/CoRN/transc/RealPowers/power_int.con.
+inline "cic:/CoRN/transc/RealPowers/power_int.con".
(* UNEXPORTED
Hint Resolve power_int: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/Exp_power.con.
+inline "cic:/CoRN/transc/RealPowers/Exp_power.con".
-inline cic:/CoRN/transc/RealPowers/mult_power.con.
+inline "cic:/CoRN/transc/RealPowers/mult_power.con".
-inline cic:/CoRN/transc/RealPowers/recip_power.con.
+inline "cic:/CoRN/transc/RealPowers/recip_power.con".
(* UNEXPORTED
Hint Resolve Exp_power mult_power recip_power: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/div_power.con.
+inline "cic:/CoRN/transc/RealPowers/div_power.con".
(* UNEXPORTED
Hint Resolve div_power: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_ap_zero.con.
+inline "cic:/CoRN/transc/RealPowers/power_ap_zero.con".
-inline cic:/CoRN/transc/RealPowers/power_mult.con.
+inline "cic:/CoRN/transc/RealPowers/power_mult.con".
-inline cic:/CoRN/transc/RealPowers/power_pos.con.
+inline "cic:/CoRN/transc/RealPowers/power_pos.con".
(* UNEXPORTED
Hint Resolve power_mult: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_recip.con.
+inline "cic:/CoRN/transc/RealPowers/power_recip.con".
(* UNEXPORTED
Hint Resolve power_recip: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_div.con.
+inline "cic:/CoRN/transc/RealPowers/power_div.con".
(* UNEXPORTED
Hint Resolve power_div: algebra.
*)
(* UNEXPORTED
-Section Power_Function.
+Section Power_Function
*)
(*#* **Power Function
%\end{convention}%
*)
-inline cic:/CoRN/transc/RealPowers/J.var.
+alias id "J" = "cic:/CoRN/transc/RealPowers/Power_Function/J.var".
-inline cic:/CoRN/transc/RealPowers/F.var.
+alias id "F" = "cic:/CoRN/transc/RealPowers/Power_Function/F.var".
-inline cic:/CoRN/transc/RealPowers/G.var.
+alias id "G" = "cic:/CoRN/transc/RealPowers/Power_Function/G.var".
-inline cic:/CoRN/transc/RealPowers/FPower.con.
+inline "cic:/CoRN/transc/RealPowers/FPower.con".
-inline cic:/CoRN/transc/RealPowers/FPower_domain.con.
+inline "cic:/CoRN/transc/RealPowers/FPower_domain.con".
-inline cic:/CoRN/transc/RealPowers/Continuous_power.con.
+inline "cic:/CoRN/transc/RealPowers/Continuous_power.con".
(* UNEXPORTED
-End Power_Function.
+End Power_Function
+*)
+
+(* NOTATION
+Notation "F {!} G" := (FPower F G) (at level 20).
*)
(* UNEXPORTED
-Section More_on_Power_Function.
+Section More_on_Power_Function
*)
(* UNEXPORTED
(*#* From global continuity we can obviously get local continuity: *)
-inline cic:/CoRN/transc/RealPowers/continuous_I_power.con.
+inline "cic:/CoRN/transc/RealPowers/continuous_I_power.con".
(*#* The rule for differentiation is a must. *)
Opaque Logarithm.
*)
-inline cic:/CoRN/transc/RealPowers/Derivative_power.con.
+inline "cic:/CoRN/transc/RealPowers/Derivative_power.con".
-inline cic:/CoRN/transc/RealPowers/Diffble_power.con.
+inline "cic:/CoRN/transc/RealPowers/Diffble_power.con".
(* UNEXPORTED
-End More_on_Power_Function.
+End More_on_Power_Function
*)
(* UNEXPORTED