We begin with some technical stuff that will be necessary for division.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var" "Lemmas__".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var" "Lemmas__".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var" "Lemmas__".
+alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var".
(* begin hide *)
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var" "Lemmas__".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var".
(* begin hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var" "Lemmas__".
+alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var".
(* end show *)
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var" "Local_Results__".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var" "Local_Results__".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var" "Local_Results__".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var".
(* begin hide *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var" "Local_Results__".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var" "Local_Results__".
+alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var" "Local_Results__".
+alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var" "Local_Results__".
+alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var" "Local_Results__".
+alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var" "Local_Results__".
+alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con".
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var" "Local_Results__".
+alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var".
(* end show *)
Section Corolaries
*)
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var" "Corolaries__".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var" "Corolaries__".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var" "Corolaries__".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var".
(* begin hide *)
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var" "Corolaries__".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var" "Corolaries__".
+alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var" "Corolaries__".
+alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var" "Corolaries__".
+alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var" "Corolaries__".
+alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var" "Corolaries__".
+alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var".
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con".
-inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var" "Corolaries__".
+alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con".
induction using the constant and addition rules.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var" "Derivative_Sums__".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var" "Derivative_Sums__".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var" "Derivative_Sums__".
+alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var" "Derivative_Sums__".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var".
(* begin hide *)