X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Ftransc%2FRealPowers.ma;h=fd081416a06d63a6b8fadb81dd41cb59cf548e21;hb=fa0d5a79683ea3966f62b21be7e1a3e274597911;hp=26a378354dbe62d3cf1006353d0ac239b360a010;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma b/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma index 26a378354..fd081416a 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma @@ -16,15 +16,15 @@ 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. @@ -39,7 +39,11 @@ $x^y=e^{y\times\log(x)}$#xy=ey*log(x)#, whenever [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 @@ -48,29 +52,29 @@ still has all the good properties of that operation; when [x [=] e] it 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. @@ -80,52 +84,52 @@ 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 @@ -137,24 +141,28 @@ on partial functions which preserves continuity. %\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 @@ -163,7 +171,7 @@ Opaque Expon Logarithm. (*#* 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. *) @@ -175,12 +183,12 @@ Transparent Logarithm. 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