--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics2".
+
+include "CoRN.ma".
+
+(* $Id: DiffTactics2.v,v 1.1.1.1 2004/02/05 16:25:45 lionelm Exp $ *)
+
+(* begin hide *)
+
+include "ftc/Differentiability.ma".
+
+(* UNEXPORTED
+Section Automatizing_Continuity
+*)
+
+alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var".
+
+alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var".
+
+inline "cic:/CoRN/tactics/DiffTactics2/cont_function.ind".
+
+inline "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con".
+
+inline "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con".
+
+(* UNEXPORTED
+End Automatizing_Continuity
+*)
+
+(* UNEXPORTED
+Ltac pfunct_to_cont a b f :=
+ match constr:f with
+ | ([-C-]?X3) => constr:(cconst a b X3)
+ | FId => constr:(cid a b)
+ | (?X3{+}?X4) =>
+ let t1 := pfunct_to_cont a b X3 with t2 := pfunct_to_cont a b X4 in
+ constr:(cplus a b t1 t2)
+ | ({--}?X3) =>
+ let t1 := pfunct_to_cont a b X3 in
+ constr:(cinv a b t1)
+ | (?X3{-}?X4) =>
+ let t1 := pfunct_to_cont a b X3 with t2 := pfunct_to_cont a b X4 in
+ constr:(cminus a b t1 t2)
+ | (?X3{*}?X4) =>
+ let t1 := pfunct_to_cont a b X3 with t2 := pfunct_to_cont a b X4 in
+ constr:(cmult a b t1 t2)
+ | (?X3{**}?X4) =>
+ let t := pfunct_to_cont a b X4 in
+ constr:(cscalmult a b X3 t)
+ | (?X3{^}?X4) =>
+ let t1 := pfunct_to_cont a b X3 in
+ constr:(cnth a b t1 X4)
+ | (FAbs ?X3) => let t1 := pfunct_to_cont a b X3 in
+ constr:(cabs a b t1)
+ | ?X3 =>
+ let t := constr:X3 in
+ match goal with
+ | Hab:_,H:(Continuous_I (a:=a) (b:=b) ?X1 t) |- _ =>
+ constr:(hyp_c a b X1 t H)
+ | H:(Derivative_I (a:=a) (b:=b) ?X1 t ?X4) |- _ =>
+ constr:(hyp_d a b X1 t X4 H)
+ | H:(Derivative_I (a:=a) (b:=b) ?X1 ?X4 t) |- _ =>
+ constr:(hyp_d' a b X1 X4 t H)
+ | H:(Diffble_I (a:=a) (b:=b) ?X1 t) |- _ =>
+ constr:(hyp_diff a b X1 t H)
+ end
+ end.
+*)
+
+(* UNEXPORTED
+Ltac New_Contin :=
+ match goal with
+ | |- (Continuous_I (a:=?X1) (b:=?X2) ?X4 ?X3) =>
+ let r := pfunct_to_cont X1 X2 X3 in
+ let a := constr:X1 in
+ let b := constr:X2 in
+ (apply Continuous_I_wd with (cont_to_pfunct a b r);
+ [ unfold cont_to_pfunct in |- * | apply continuous_cont ])
+ end.
+*)
+
+(* UNEXPORTED
+Section Automatizing_Derivatives
+*)
+
+alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var".
+
+alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var".
+
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind".
+
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con".
+
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con".
+
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con".
+
+inline "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con".
+
+(* UNEXPORTED
+End Automatizing_Derivatives
+*)
+
+(* UNEXPORTED
+Ltac pfunct_to_restr a b f :=
+ match constr:f with
+ | ([-C-]?X3) => constr:(const a b X3)
+ | FId => constr:(id a b)
+ | (?X3{+}?X4) =>
+ let t1 := pfunct_to_restr a b X3 with t2 := pfunct_to_restr a b X4 in
+ constr:(rplus a b t1 t2)
+ | ({--}?X3) =>
+ let t1 := pfunct_to_restr a b X3 in
+ constr:(rinv a b t1)
+ | (?X3{-}?X4) =>
+ let t1 := pfunct_to_restr a b X3 with t2 := pfunct_to_restr a b X4 in
+ constr:(rminus a b t1 t2)
+ | (?X3{*}?X4) =>
+ let t1 := pfunct_to_restr a b X3 with t2 := pfunct_to_restr a b X4 in
+ constr:(rmult a b t1 t2)
+ | (?X3{**}?X4) =>
+ let t := pfunct_to_restr a b X4 in
+ constr:(rscalmult a b X3 t)
+ | (?X3{^}?X4) =>
+ let t1 := pfunct_to_restr a b X3 in
+ constr:(rnth a b t1 X4)
+ | ?X3 =>
+ let t := constr:X3 in
+ match goal with
+ | H:(Derivative_I (a:=a) (b:=b) ?X1 t ?X4) |- _ =>
+ constr:(hyp a b X1 t X4 H)
+ | H:(Diffble_I (a:=a) (b:=b) ?X1 t) |- _ => constr:(
+ hyp' a b X1 t H)
+ end
+ end.
+*)
+
+(* UNEXPORTED
+Ltac New_Deriv :=
+ match goal with
+ | |- (Derivative_I (a:=?X1) (b:=?X2) _ ?X3 ?X4) =>
+ let r := pfunct_to_restr X1 X2 X3 in
+ (apply Derivative_I_wdl with (deriv_to_pfunct X1 X2 r);
+ [ unfold deriv_to_pfunct in |- *
+ | apply Derivative_I_wdr with (deriv_deriv X1 X2 r);
+ [ unfold deriv_deriv, deriv_to_pfunct in |- *
+ | apply deriv_restr ] ])
+ end.
+*)
+
+(* UNEXPORTED
+Ltac Differentiate :=
+ match goal with
+ | |- (Diffble_I (a:=?X1) (b:=?X2) _ ?X3) =>
+ let r := pfunct_to_restr X1 X2 X3 in
+ (apply Diffble_I_wd with (deriv_to_pfunct X1 X2 r);
+ [ apply diffble_restr | unfold deriv_deriv, deriv_to_pfunct in |- * ])
+ end.
+*)
+
+(* UNEXPORTED
+Ltac derivative_of f :=
+ match constr:f with
+ | ([-C-]?X3) => constr:([-C-]ZeroR)
+ | FId => constr:([-C-]OneR)
+ | (?X3{+}?X4) =>
+ let t1 := derivative_of X3 with t2 := derivative_of X4 in
+ constr:(t1{+}t2)
+ | ({--}?X3) => let t1 := derivative_of X3 in
+ constr:({--}t1)
+ | (?X3{-}?X4) =>
+ let t1 := derivative_of X3 with t2 := derivative_of X4 in
+ constr:(t1{-}t2)
+ | (?X3{*}?X4) =>
+ let t1 := derivative_of X3
+ with t2 := derivative_of X4
+ with t3 := constr:X3
+ with t4 := constr:X4 in
+ constr:(t3{*}t2{+}t1{*}t4)
+ | (?X3{**}?X4) =>
+ let t1 := derivative_of X4 with t2 := constr:X3 in
+ constr:(t2{**}t1)
+ | (?X3{^}0) => constr:([-C-]ZeroR)
+ | (?X3{^}S ?X4) =>
+ let t1 := derivative_of X3 with t2 := constr:X3 with t3 := constr:X4 in
+ constr:(nring _ (S t3){**}(t1{*}t2{^}t3))
+ | ({1/}?X3) =>
+ let t1 := derivative_of X3 with t2 := constr:X3 in
+ constr:({--}(t1{/}t2{*}t2))
+ | (?X3{/}?X4) =>
+ let t1 := derivative_of X3
+ with t2 := derivative_of X4
+ with t3 := constr:X3
+ with t4 := constr:X4 in
+ constr:((t1{*}t4{-}t3{*}t2){/}t4{*}t4)
+ | (?X3[o]?X4) =>
+ let t1 := derivative_of X3
+ with t2 := derivative_of X4
+ with t3 := constr:X3 in
+ constr:((t3[o]t2){*}t1)
+ | ?X3 =>
+ let t := constr:X3 in
+ match goal with
+ | H:(Derivative_I (b:=t) ?X4) |- _ =>
+ let t1 := constr:X4 in
+ constr:t1
+ end
+ end.
+*)
+
+(* UNEXPORTED
+Ltac Deriv_I_substR :=
+ match goal with
+ | |- (Derivative_I _ ?X1 _) =>
+ let t := derivative_of X1 in
+ apply Derivative_I_wdr with t
+ end.
+*)
+
+(* end hide *)
+
projects / helm.git / blobdiff