(* chapter 'Biegelinie' from the textbook: 

   Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.

   author: Walther Neuper

   050826,

   (c) due to copyright terms

*)

theory Biegelinie imports Integrate Equation EqSystem begin

consts

  q_    :: real => real ("q'_")     (* Streckenlast               *)

  Q     :: real => real             (* Querkraft                  *)

  Q'    :: real => real             (* Ableitung der Querkraft    *)

  M'_b  :: real => real ("M'_b")    (* Biegemoment                *)

  M'_b' :: real => real ("M'_b'")   (* Ableitung des Biegemoments *)

  y''   :: real => real             (* 2.Ableitung der Biegeline  *)

  y'    :: real => real             (* Neigung der Biegeline      *)

(*y     :: real => real             (* Biegeline                  *)*)

  EI    :: real                     (* Biegesteifigkeit           *)

  (*new Descriptions in the related problems*)

  Traegerlaenge            :: real => una

  Streckenlast             :: real => una

  BiegemomentVerlauf       :: bool => una

  Biegelinie               :: (real => real) => una

  Randbedingungen          :: bool list => una

  RandbedingungenBiegung   :: bool list => una

  RandbedingungenNeigung   :: bool list => una

  RandbedingungenMoment    :: bool list => una

  RandbedingungenQuerkraft :: bool list => una

  FunktionsVariable        :: real => una

  Funktionen               :: bool list => una

  Gleichungen              :: bool list => una

  (*Script-names*)

  Biegelinie2Script        :: "[real,real,real,real=>real,bool list,

				bool] => bool"	

	("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)

  BiegelinieScript         :: "[real,real,real,real=>real,bool list,bool list,

				bool] => bool"	

	("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)

  Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,

				bool] => bool"		

	("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)

  Biege4x4SystemScript     :: "[real,real,real,real=>real,bool list,  

				bool] => bool"	

	("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)

  Biege1xIntegrierenScript :: 

	            "[real,real,real,real=>real,bool list,bool list,bool list,

		      bool] => bool"	

	("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)

  Belastung2BiegelScript   :: "[real,real,

	                        bool list] => bool list"	

	("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)

  SetzeRandbedScript       :: "[bool list,bool list,

	                        bool list] => bool list"	

	("((Script SetzeRandbedScript (_ _ =))// (_))" 9)

axioms

  Querkraft_Belastung:   "Q' x = -q_ x"

  Belastung_Querkraft:   "-q_ x = Q' x"

  Moment_Querkraft:      "M_b' x = Q x"

  Querkraft_Moment:      "Q x = M_b' x"

  Neigung_Moment:        "y'' x = -M_b x/ EI"

  Moment_Neigung:        "M_b x = -EI * y'' x"

  (*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)

  make_fun_explicit:     "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"

ML {*

val thy = @{theory};

(** theory elements for transfer into html **)

store_isa ["IsacKnowledge"] [];

store_thy thy 

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_isa ["IsacKnowledge", theory2thyID thy, "Theorems"] 

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Belastung_Querkraft", Belastung_Querkraft)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Moment_Neigung", Moment_Neigung)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Moment_Querkraft", Moment_Querkraft)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Neigung_Moment", Neigung_Moment)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Querkraft_Belastung", Querkraft_Belastung)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("Querkraft_Moment", Querkraft_Moment)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

store_thm thy ("make_fun_explicit", make_fun_explicit)

	  ["Walther Neuper 2005 supported by a grant from NMI Austria"];

(** problems **)

store_pbt

 (prep_pbt thy "pbl_bieg" [] e_pblID

 (["Biegelinien"],

  [("#Given" ,["Traegerlaenge l_", "Streckenlast q__"]),

   (*("#Where",["0 < l_"]), ...wait for &lt; and handling Arbfix*)

   ("#Find"  ,["Biegelinie b_"]),

   ("#Relate",["Randbedingungen rb_"])

  ],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["IntegrierenUndKonstanteBestimmen2"]]));

store_pbt 

 (prep_pbt thy "pbl_bieg_mom" [] e_pblID

 (["MomentBestimmte","Biegelinien"],

  [("#Given" ,["Traegerlaenge l_", "Streckenlast q__"]),

   (*("#Where",["0 < l_"]), ...wait for &lt; and handling Arbfix*)

   ("#Find"  ,["Biegelinie b_"]),

   ("#Relate",["RandbedingungenBiegung rb_","RandbedingungenMoment rm_"])

  ],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["IntegrierenUndKonstanteBestimmen"]]));

store_pbt

 (prep_pbt thy "pbl_bieg_momg" [] e_pblID

 (["MomentGegebene","Biegelinien"],

  [],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]]));

store_pbt

 (prep_pbt thy "pbl_bieg_einf" [] e_pblID

 (["einfache","Biegelinien"],

  [],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["IntegrierenUndKonstanteBestimmen","4x4System"]]));

store_pbt

 (prep_pbt thy "pbl_bieg_momquer" [] e_pblID

 (["QuerkraftUndMomentBestimmte","Biegelinien"],

  [],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]]));

store_pbt

 (prep_pbt thy "pbl_bieg_vonq" [] e_pblID

 (["vonBelastungZu","Biegelinien"],

  [("#Given" ,["Streckenlast q__","FunktionsVariable v_v"]),

   ("#Find"  ,["Funktionen funs___"])],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["Biegelinien","ausBelastung"]]));

store_pbt

 (prep_pbt thy "pbl_bieg_randbed" [] e_pblID

 (["setzeRandbedingungen","Biegelinien"],

  [("#Given" ,["Funktionen funs_","Randbedingungen rb_"]),

   ("#Find"  ,["Gleichungen equs___"])],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["Biegelinien","setzeRandbedingungenEin"]]));

store_pbt

 (prep_pbt thy "pbl_equ_fromfun" [] e_pblID

 (["makeFunctionTo","equation"],

  [("#Given" ,["functionEq fun_","substitution sub_"]),

   ("#Find"  ,["equality equ___"])],

  append_rls "e_rls" e_rls [], 

  NONE, 

  [["Equation","fromFunction"]]));

(** methods **)

val srls = Rls {id="srls_IntegrierenUnd..", 

		preconds = [], 

		rew_ord = ("termlessI",termlessI), 

		erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls

				  [(*for asm in nth_Cons_ ...*)

				   Calc ("op <",eval_equ "#less_"),

				   (*2nd nth_Cons_ pushes n+-1 into asms*)

				   Calc("op +", eval_binop "#add_")

				   ], 

		srls = Erls, calc = [],

		rules = [Thm ("nth_Cons_",num_str @{thm nth_Cons_}),

			 Calc("op +", eval_binop "#add_"),

			 Thm ("nth_Nil_",num_str @{thm nth_Nil_}),

			 Calc("Tools.lhs", eval_lhs"eval_lhs_"),

			 Calc("Tools.rhs", eval_rhs"eval_rhs_"),

			 Calc("Atools.argument'_in",

			      eval_argument_in "Atools.argument'_in")

			 ],

		scr = EmptyScr};

val srls2 = 

    Rls {id="srls_IntegrierenUnd..", 

	 preconds = [], 

	 rew_ord = ("termlessI",termlessI), 

	 erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls

			   [(*for asm in nth_Cons_ ...*)

			    Calc ("op <",eval_equ "#less_"),

			    (*2nd nth_Cons_ pushes n+-1 into asms*)

			    Calc("op +", eval_binop "#add_")

			    ], 

	 srls = Erls, calc = [],

	 rules = [Thm ("nth_Cons_",num_str @{thm nth_Cons_}),

		  Calc("op +", eval_binop "#add_"),

		  Thm ("nth_Nil_", num_str @{thm nth_Nil_}),

		  Calc("Tools.lhs", eval_lhs "eval_lhs_"),

		  Calc("Atools.filter'_sameFunId",

		       eval_filter_sameFunId "Atools.filter'_sameFunId"),

		  (*WN070514 just for smltest/../biegelinie.sml ...*)

		  Calc("Atools.sameFunId", eval_sameFunId "Atools.sameFunId"),

		  Thm ("filter_Cons", num_str @{thm filter_Cons}),

		  Thm ("filter_Nil", num_str @{thm filter_Nil}),

		  Thm ("if_True", num_str @{thm if_True}),

		  Thm ("if_False", num_str @{thm if_False}),

		  Thm ("hd_thm", num_str @{thm hd_thm})

		  ],

	 scr = EmptyScr};

store_met

    (prep_met thy "met_biege" [] e_metID

	      (["IntegrierenUndKonstanteBestimmen"],

	       [("#Given" ,["Traegerlaenge l_", "Streckenlast q__",

			    "FunktionsVariable v_v"]),

		(*("#Where",["0 < l_"]), ...wait for &lt; and handling Arbfix*)

		("#Find"  ,["Biegelinie b_"]),

		("#Relate",["RandbedingungenBiegung rb_",

			    "RandbedingungenMoment rm_"])

		],

	       {rew_ord'="tless_true", 

		rls' = append_rls "erls_IntegrierenUndK.." e_rls 

				  [Calc ("Atools.ident",eval_ident "#ident_"),

				   Thm ("not_true",num_str @{thm not_true}),

				   Thm ("not_false",num_str @{thm not_false})], 

		calc = [], srls = srls, prls = Erls,

		crls = Atools_erls, nrls = Erls},

"Script BiegelinieScript                                                  " ^

"(l_::real) (q__::real) (v_v::real) (b_::real=>real)                       " ^

"(rb_::bool list) (rm_::bool list) =                                      " ^

"  (let q___ = Take (q_ v_v = q__);                                        " ^

"       q___ = ((Rewrite sym_real_minus_eq_cancel True) @@                " ^

"              (Rewrite Belastung_Querkraft True)) q___;                  " ^

"      (Q__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs q___), real_ v_v, real_real_ Q]);   " ^

"       Q__ = Rewrite Querkraft_Moment True Q__;                          " ^

"      (M__::bool) =                                                      " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs Q__), real_ v_v, real_real_ M_b]);  " ^

"       e1__ = nth_ 1 rm_;                                                " ^

"      (x1__::real) = argument_in (lhs e1__);                             " ^

"      (M1__::bool) = (Substitute [v_ = x1__]) M__;                       " ^

"       M1__        = (Substitute [e1__]) M1__ ;                          " ^

"       M2__ = Take M__;                                                  " ^

(*without this Take 'Substitute [v_ = x2__]' takes _last formula from ctree_*)

"       e2__ = nth_ 2 rm_;                                                " ^

"      (x2__::real) = argument_in (lhs e2__);                             " ^

"      (M2__::bool) = ((Substitute [v_ = x2__]) @@                        " ^

"                      (Substitute [e2__])) M2__;                         " ^

"      (c_1_2__::bool list) =                                             " ^

"             (SubProblem (Biegelinie_,[linear,system],[no_met])          " ^

"                          [booll_ [M1__, M2__], reall [c,c_2]]);         " ^

"       M__ = Take  M__;                                                  " ^

"       M__ = ((Substitute c_1_2__) @@                                    " ^

"              (Try (Rewrite_Set_Inst [(bdv_1, c),(bdv_2, c_2)]" ^

"                                   simplify_System False)) @@ " ^

"              (Rewrite Moment_Neigung False) @@ " ^

"              (Rewrite make_fun_explicit False)) M__;                    " ^

(*----------------------- and the same once more ------------------------*)

"      (N__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs M__), real_ v_v, real_real_ y']);   " ^

"      (B__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs N__), real_ v_v, real_real_ y]);    " ^

"       e1__ = nth_ 1 rb_;                                                " ^

"      (x1__::real) = argument_in (lhs e1__);                             " ^

"      (B1__::bool) = (Substitute [v_ = x1__]) B__;                       " ^

"       B1__        = (Substitute [e1__]) B1__ ;                          " ^

"       B2__ = Take B__;                                                  " ^

"       e2__ = nth_ 2 rb_;                                                " ^

"      (x2__::real) = argument_in (lhs e2__);                             " ^

"      (B2__::bool) = ((Substitute [v_ = x2__]) @@                        " ^

"                      (Substitute [e2__])) B2__;                         " ^

"      (c_1_2__::bool list) =                                             " ^

"             (SubProblem (Biegelinie_,[linear,system],[no_met])          " ^

"                          [booll_ [B1__, B2__], reall [c,c_2]]);         " ^

"       B__ = Take  B__;                                                  " ^

"       B__ = ((Substitute c_1_2__) @@                                    " ^

"              (Rewrite_Set_Inst [(bdv, x)] make_ratpoly_in False)) B__   " ^

" in B__)"

));

store_met

    (prep_met thy "met_biege_2" [] e_metID

	      (["IntegrierenUndKonstanteBestimmen2"],

	       [("#Given" ,["Traegerlaenge l_", "Streckenlast q__",

			    "FunktionsVariable v_v"]),

		(*("#Where",["0 < l_"]), ...wait for &lt; and handling Arbfix*)

		("#Find"  ,["Biegelinie b_"]),

		("#Relate",["Randbedingungen rb_"])

		],

	       {rew_ord'="tless_true", 

		rls' = append_rls "erls_IntegrierenUndK.." e_rls 

				  [Calc ("Atools.ident",eval_ident "#ident_"),

				   Thm ("not_true",num_str @{thm not_true}),

				   Thm ("not_false",num_str @{thm not_false})], 

		calc = [], 

		srls = append_rls "erls_IntegrierenUndK.." e_rls 

				  [Calc("Tools.rhs", eval_rhs"eval_rhs_"),

				   Calc ("Atools.ident",eval_ident "#ident_"),

				   Thm ("last_thmI",num_str @{thm last_thmI}),

				   Thm ("if_True",num_str @{thm if_True}),

				   Thm ("if_False",num_str @{thm if_False})

				   ],

		prls = Erls, crls = Atools_erls, nrls = Erls},

"Script Biegelinie2Script                                                 " ^

"(l_::real) (q__::real) (v_v::real) (b_::real=>real) (rb_::bool list) =    " ^

"  (let                                                                   " ^

"      (funs_:: bool list) =                                              " ^

"             (SubProblem (Biegelinie_,[vonBelastungZu,Biegelinien],      " ^

"                          [Biegelinien,ausBelastung])                    " ^

"                          [real_ q__, real_ v_]);                        " ^

"      (equs_::bool list) =                                               " ^

"             (SubProblem (Biegelinie_,[setzeRandbedingungen,Biegelinien]," ^

"                          [Biegelinien,setzeRandbedingungenEin])         " ^

"                          [booll_ funs_, booll_ rb_]);                   " ^

"      (cons_::bool list) =                                               " ^

"             (SubProblem (Biegelinie_,[linear,system],[no_met])          " ^

"                          [booll_ equs_, reall [c,c_2,c_3,c_4]]);        " ^

"       B_ = Take (lastI funs_);                                          " ^

"       B_ = ((Substitute cons_) @@                                       " ^

"              (Rewrite_Set_Inst [(bdv, v_v)] make_ratpoly_in False)) B_   " ^

" in B_)"

));

store_met

    (prep_met thy "met_biege_intconst_2" [] e_metID

	      (["IntegrierenUndKonstanteBestimmen","2xIntegrieren"],

	       [],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = e_rls, 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

"empty_script"

));

store_met

    (prep_met thy "met_biege_intconst_4" [] e_metID

	      (["IntegrierenUndKonstanteBestimmen","4x4System"],

	       [],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = e_rls, 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

"empty_script"

));

store_met

    (prep_met thy "met_biege_intconst_1" [] e_metID

	      (["IntegrierenUndKonstanteBestimmen","1xIntegrieren"],

	       [],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = e_rls, 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

"empty_script"

));

store_met

    (prep_met thy "met_biege2" [] e_metID

	      (["Biegelinien"],

	       [],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = e_rls, 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

"empty_script"

));

store_met

    (prep_met thy "met_biege_ausbelast" [] e_metID

	      (["Biegelinien","ausBelastung"],

	       [("#Given" ,["Streckenlast q__","FunktionsVariable v_v"]),

		("#Find"  ,["Funktionen funs_"])],

	       {rew_ord'="tless_true", 

		rls' = append_rls "erls_ausBelastung" e_rls 

				  [Calc ("Atools.ident",eval_ident "#ident_"),

				   Thm ("not_true",num_str @{thm not_true}),

				   Thm ("not_false",num_str @{thm not_false})], 

		calc = [], 

		srls = append_rls "srls_ausBelastung" e_rls 

				  [Calc("Tools.rhs", eval_rhs"eval_rhs_")], 

		prls = e_rls, crls = Atools_erls, nrls = e_rls},

"Script Belastung2BiegelScript (q__::real) (v_v::real) =                   " ^

"  (let q___ = Take (q_ v_v = q__);                                        " ^

"       q___ = ((Rewrite sym_real_minus_eq_cancel True) @@                " ^

"              (Rewrite Belastung_Querkraft True)) q___;                  " ^

"      (Q__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs q___), real_ v_v, real_real_ Q]);   " ^

"       M__ = Rewrite Querkraft_Moment True Q__;                          " ^

"      (M__::bool) =                                                      " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs M__), real_ v_v, real_real_ M_b]);  " ^

"       N__ = ((Rewrite Moment_Neigung False) @@                          " ^

"              (Rewrite make_fun_explicit False)) M__;                    " ^

"      (N__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs N__), real_ v_v, real_real_ y']);   " ^

"      (B__:: bool) =                                                     " ^

"             (SubProblem (Biegelinie_,[named,integrate,function],        " ^

"                          [diff,integration,named])                      " ^

"                          [real_ (rhs N__), real_ v_v, real_real_ y])     " ^

" in [Q__, M__, N__, B__])"

));

store_met

    (prep_met thy "met_biege_setzrand" [] e_metID

	      (["Biegelinien","setzeRandbedingungenEin"],

	       [("#Given" ,["Funktionen funs_","Randbedingungen rb_"]),

		("#Find"  ,["Gleichungen equs___"])],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = srls2, 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

"Script SetzeRandbedScript (funs_::bool list) (rb_::bool list) = " ^

" (let b1_ = nth_ 1 rb_;                                         " ^

"      fs_ = filter_sameFunId (lhs b1_) funs_;                   " ^

"      (e1_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b1_]);         " ^

"      b2_ = nth_ 2 rb_;                                         " ^

"      fs_ = filter_sameFunId (lhs b2_) funs_;                   " ^

"      (e2_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b2_]);         " ^

"      b3_ = nth_ 3 rb_;                                         " ^

"      fs_ = filter_sameFunId (lhs b3_) funs_;                   " ^

"      (e3_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b3_]);         " ^

"      b4_ = nth_ 4 rb_;                                         " ^

"      fs_ = filter_sameFunId (lhs b4_) funs_;                   " ^

"      (e4_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b4_])          " ^

" in [e1_,e2_,e3_,e4_])"

(* filter requires more than 1 sec !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

"Script SetzeRandbedScript (funs_::bool list) (rb_::bool list) = " ^

" (let b1_ = nth_ 1 rb_;                                         " ^

"      fs_ = filter (sameFunId (lhs b1_)) funs_;                 " ^

"      (e1_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b1_]);         " ^

"      b2_ = nth_ 2 rb_;                                         " ^

"      fs_ = filter (sameFunId (lhs b2_)) funs_;                 " ^

"      (e2_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b2_]);         " ^

"      b3_ = nth_ 3 rb_;                                         " ^

"      fs_ = filter (sameFunId (lhs b3_)) funs_;                 " ^

"      (e3_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b3_]);         " ^

"      b4_ = nth_ 4 rb_;                                         " ^

"      fs_ = filter (sameFunId (lhs b4_)) funs_;                 " ^

"      (e4_::bool) =                                             " ^

"             (SubProblem (Biegelinie_,[makeFunctionTo,equation]," ^

"                          [Equation,fromFunction])              " ^

"                          [bool_ (hd fs_), bool_ b4_])          " ^

" in [e1_,e2_,e3_,e4_])"*)

));

store_met

    (prep_met thy "met_equ_fromfun" [] e_metID

	      (["Equation","fromFunction"],

	       [("#Given" ,["functionEq fun_","substitution sub_"]),

		("#Find"  ,["equality equ___"])],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = append_rls "srls_in_EquationfromFunc" e_rls

				  [Calc("Tools.lhs", eval_lhs"eval_lhs_"),

				   Calc("Atools.argument'_in",

					eval_argument_in

					    "Atools.argument'_in")], 

		prls=e_rls,

	     crls = Atools_erls, nrls = e_rls},

(*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->

       0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)

"Script Function2Equality (fun_::bool) (sub_::bool) =" ^

" (let fun_ = Take fun_;                             " ^

"      bdv_ = argument_in (lhs fun_);                " ^

"      val_ = argument_in (lhs sub_);                " ^

"      equ_ = (Substitute [bdv_ = val_]) fun_;       " ^

"      equ_ = (Substitute [sub_]) fun_               " ^

" in (Rewrite_Set norm_Rational False) equ_)             "

));

*}

end