neuper@37906
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(*. (c) by Richard Lang, 2003 .*)
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neuper@37906
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(* theory collecting all knowledge for LinearEquations
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neuper@37906
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created by: rlang
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neuper@37906
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date: 02.10
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neuper@37906
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changed by: rlang
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neuper@37906
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last change by: rlang
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neuper@37906
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date: 02.10.20
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neuper@37906
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*)
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neuper@37906
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neuper@37950
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theory LinEq imports Poly Equation begin
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neuper@37906
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neuper@52148
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axiomatization where
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wneuper@59370
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(*-- normalise --*)
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neuper@37906
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(*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
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neuper@52148
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all_left: "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)" and
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walther@60242
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makex1_x: "a \<up> 1 = a" and
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neuper@52148
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real_assoc_1: "a+(b+c) = a+b+c" and
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neuper@52148
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real_assoc_2: "a*(b*c) = a*b*c" and
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neuper@37906
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neuper@37906
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(*-- solve --*)
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neuper@52148
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lin_isolate_add1: "(a + b*bdv = 0) = (b*bdv = (-1)*a)" and
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neuper@52148
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lin_isolate_add2: "(a + bdv = 0) = ( bdv = (-1)*a)" and
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neuper@37982
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lin_isolate_div: "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"
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neuper@37950
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wneuper@59472
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ML \<open>
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neuper@37950
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val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
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walther@59852
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Rule_Set.append_rules "LinEq_prls" Rule_Set.empty
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wenzelm@60294
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[\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
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wenzelm@60294
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\<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches ""),
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wenzelm@60294
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\<^rule_eval>\<open>Prog_Expr.lhs\<close> (Prog_Expr.eval_lhs ""),
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wenzelm@60294
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\<^rule_eval>\<open>Prog_Expr.rhs\<close> (Prog_Expr.eval_rhs ""),
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wenzelm@60294
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\<^rule_eval>\<open>has_degree_in\<close> (eval_has_degree_in ""),
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wenzelm@60294
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\<^rule_eval>\<open>is_polyrat_in\<close> (eval_is_polyrat_in ""),
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wenzelm@60294
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\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
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wenzelm@60294
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\<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
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walther@59871
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Rule.Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
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walther@59871
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Rule.Thm ("not_false",ThmC.numerals_to_Free @{thm not_false}),
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walther@59871
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Rule.Thm ("and_true",ThmC.numerals_to_Free @{thm and_true}),
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walther@59871
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Rule.Thm ("and_false",ThmC.numerals_to_Free @{thm and_false}),
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walther@59871
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Rule.Thm ("or_true",ThmC.numerals_to_Free @{thm or_true}),
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walther@59871
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Rule.Thm ("or_false",ThmC.numerals_to_Free @{thm or_false})
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neuper@37950
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];
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neuper@37950
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(* ----- erls ----- *)
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neuper@37950
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val LinEq_crls =
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walther@59852
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Rule_Set.append_rules "LinEq_crls" poly_crls
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walther@59871
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[Rule.Thm ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1})
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neuper@37950
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(*
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neuper@37950
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Don't use
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wenzelm@60294
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\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
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wenzelm@60294
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\<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
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neuper@37950
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*)
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neuper@37950
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];
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neuper@37950
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neuper@37950
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(* ----- crls ----- *)
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neuper@37950
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val LinEq_erls =
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walther@59852
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Rule_Set.append_rules "LinEq_erls" Poly_erls
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walther@59871
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[Rule.Thm ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1})
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neuper@37950
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(*
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neuper@37950
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Don't use
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wenzelm@60294
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\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
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wenzelm@60294
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\<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
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neuper@37950
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*)
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neuper@37950
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];
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wneuper@59472
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\<close>
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wenzelm@60289
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rule_set_knowledge LinEq_erls = LinEq_erls
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wneuper@59472
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ML \<open>
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neuper@37950
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s1210629013@55444
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val LinPoly_simplify = prep_rls'(
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walther@59851
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Rule_Def.Repeat {id = "LinPoly_simplify", preconds = [],
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neuper@37950
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rew_ord = ("termlessI",termlessI),
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neuper@37950
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erls = LinEq_erls,
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walther@59851
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srls = Rule_Set.Empty,
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neuper@42451
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calc = [], errpatts = [],
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neuper@37950
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rules = [
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walther@59871
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Rule.Thm ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1}),
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wenzelm@60294
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\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
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wenzelm@60294
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\<^rule_eval>\<open>minus\<close> (**)(eval_binop "#sub_"),
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wenzelm@60294
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\<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
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wenzelm@60294
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(* Don't use
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wenzelm@60294
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\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
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wenzelm@60294
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\<^rule_eval>\<open>sqrt\<close> (eval_sqrt "#sqrt_"),
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neuper@37950
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*)
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wenzelm@60294
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\<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_")
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neuper@37950
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],
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walther@59878
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scr = Rule.Empty_Prog});
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wneuper@59472
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\<close>
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wenzelm@60289
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rule_set_knowledge LinPoly_simplify = LinPoly_simplify
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wneuper@59472
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ML \<open>
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neuper@37950
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neuper@37950
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(*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
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s1210629013@55444
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val LinEq_simplify = prep_rls'(
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walther@59851
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Rule_Def.Repeat {id = "LinEq_simplify", preconds = [],
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walther@59857
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rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
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neuper@37950
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erls = LinEq_erls,
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walther@59851
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srls = Rule_Set.Empty,
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neuper@42451
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calc = [], errpatts = [],
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neuper@37950
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rules = [
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walther@59871
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Rule.Thm("lin_isolate_add1",ThmC.numerals_to_Free @{thm lin_isolate_add1}),
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neuper@37950
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(* a+bx=0 -> bx=-a *)
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walther@59871
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Rule.Thm("lin_isolate_add2",ThmC.numerals_to_Free @{thm lin_isolate_add2}),
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neuper@37950
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(* a+ x=0 -> x=-a *)
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walther@59871
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Rule.Thm("lin_isolate_div",ThmC.numerals_to_Free @{thm lin_isolate_div})
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neuper@37950
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(* bx=c -> x=c/b *)
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neuper@37950
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],
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walther@59878
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scr = Rule.Empty_Prog});
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wneuper@59472
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\<close>
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wenzelm@60289
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rule_set_knowledge LinEq_simplify = LinEq_simplify
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neuper@37950
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neuper@37950
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(*----------------------------- problem types --------------------------------*)
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neuper@37950
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(* ---------linear----------- *)
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wneuper@59472
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setup \<open>KEStore_Elems.add_pbts
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wenzelm@60290
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[(Problem.prep_input @{theory} "pbl_equ_univ_lin" [] Problem.id_empty
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s1210629013@55339
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(["LINEAR", "univariate", "equation"],
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s1210629013@55339
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[("#Given" ,["equality e_e", "solveFor v_v"]),
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("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
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"Not( (lhs e_e) is_polyrat_in v_v)",
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"Not( (rhs e_e) is_polyrat_in v_v)",
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"((lhs e_e) has_degree_in v_v)=1",
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s1210629013@55339
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"((rhs e_e) has_degree_in v_v)=1"]),
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("#Find" ,["solutions v_v'i'"])],
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wneuper@59472
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LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))]\<close>
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neuper@37950
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s1210629013@55373
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(*-------------- methods------------------------------------------------------*)
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wneuper@59472
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setup \<open>KEStore_Elems.add_mets
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wenzelm@60290
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[MethodC.prep_input @{theory} "met_eqlin" [] MethodC.id_empty
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s1210629013@55373
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(["LinEq"], [],
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walther@59852
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{rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule_Set.empty, prls = Rule_Set.empty,
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crls = LinEq_crls, errpats = [], nrls = norm_Poly},
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wneuper@59545
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@{thm refl})]
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wneuper@59473
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\<close>
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walther@59997
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(* ansprechen mit ["LinEq", "solve_univar_equation"] *)
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wneuper@59545
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wneuper@59504
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partial_function (tailrec) solve_linear_equation :: "bool \<Rightarrow> real \<Rightarrow> bool list"
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wneuper@59504
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where
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walther@59635
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"solve_linear_equation e_e v_v = (
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walther@59635
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let
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walther@59635
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e_e = (
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walther@59637
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(Try (Rewrite ''all_left'')) #>
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walther@59637
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(Try (Repeat (Rewrite ''makex1_x''))) #>
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walther@59637
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(Try (Rewrite_Set ''expand_binoms'')) #>
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walther@59637
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(Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
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walther@59635
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(Try (Repeat (Rewrite_Set ''LinPoly_simplify''))) ) e_e;
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walther@59635
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e_e = (
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walther@59637
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(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''LinEq_simplify'')) #>
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walther@59635
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(Repeat (Try (Rewrite_Set ''LinPoly_simplify''))) ) e_e
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walther@59635
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in
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walther@59635
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Or_to_List e_e)"
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wneuper@59473
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setup \<open>KEStore_Elems.add_mets
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wenzelm@60290
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[MethodC.prep_input @{theory} "met_eq_lin" [] MethodC.id_empty
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walther@59997
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(["LinEq", "solve_lineq_equation"],
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s1210629013@55373
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[("#Given", ["equality e_e", "solveFor v_v"]),
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s1210629013@55373
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("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e) has_degree_in v_v) = 1"]),
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s1210629013@55373
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("#Find", ["solutions v_v'i'"])],
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walther@59852
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{rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule_Set.empty, prls = LinEq_prls, calc = [],
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s1210629013@55373
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crls = LinEq_crls, errpats = [], nrls = norm_Poly},
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wneuper@59551
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@{thm solve_linear_equation.simps})]
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wneuper@59472
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\<close>
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walther@60278
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ML \<open>
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walther@60278
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MethodC.from_store' @{theory} ["LinEq", "solve_lineq_equation"];
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walther@60278
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\<close> ML \<open>
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walther@60278
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\<close> ML \<open>
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walther@60278
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\<close>
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neuper@37950
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neuper@37906
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end
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neuper@37906
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