--- a/src/HOL/Real/real_arith.ML Thu Dec 21 18:53:32 2000 +0100
+++ b/src/HOL/Real/real_arith.ML Thu Dec 21 18:57:12 2000 +0100
@@ -3,49 +3,16 @@
Author: Tobias Nipkow, TU Muenchen
Copyright 1999 TU Muenchen
-Instantiation of the generic linear arithmetic package for type real.
+Augmentation of real linear arithmetic with rational coefficient handling
*)
local
(* reduce contradictory <= to False *)
-val simps = [order_less_irrefl, zero_eq_numeral_0, one_eq_numeral_1,
- add_real_number_of, minus_real_number_of, diff_real_number_of,
- mult_real_number_of, eq_real_number_of, less_real_number_of,
- le_real_number_of_eq_not_less, real_diff_def,
- real_minus_add_distrib, real_minus_minus];
-
-val add_rules =
- map rename_numerals
- [real_add_zero_left, real_add_zero_right,
- real_add_minus, real_add_minus_left,
- real_mult_0, real_mult_0_right,
- real_mult_1, real_mult_1_right,
- real_mult_minus_1, real_mult_minus_1_right];
-
-val simprocs = [Real_Times_Assoc.conv, Real_Numeral_Simprocs.combine_numerals]@
- Real_Numeral_Simprocs.cancel_numerals(* @ real_cancel_numeral_factors*);
+val simps = [True_implies_equals,inst "w" "number_of ?v" real_add_mult_distrib2,
+ real_divide_1,real_times_divide1_eq,real_times_divide2_eq];
-val mono_ss = simpset() addsimps
- [real_add_le_mono,real_add_less_mono,
- real_add_less_le_mono,real_add_le_less_mono];
-
-val add_mono_thms_real =
- map (fn s => prove_goal (the_context ()) s
- (fn prems => [cut_facts_tac prems 1, asm_simp_tac mono_ss 1]))
- ["(i <= j) & (k <= l) ==> i + k <= j + (l::real)",
- "(i = j) & (k <= l) ==> i + k <= j + (l::real)",
- "(i <= j) & (k = l) ==> i + k <= j + (l::real)",
- "(i = j) & (k = l) ==> i + k = j + (l::real)",
- "(i < j) & (k = l) ==> i + k < j + (l::real)",
- "(i = j) & (k < l) ==> i + k < j + (l::real)",
- "(i < j) & (k <= l) ==> i + k < j + (l::real)",
- "(i <= j) & (k < l) ==> i + k < j + (l::real)",
- "(i < j) & (k < l) ==> i + k < j + (l::real)"];
-
-val real_arith_simproc_pats =
- map (fn s => Thm.read_cterm (Theory.sign_of (the_context ())) (s, HOLogic.boolT))
- ["(m::real) < n","(m::real) <= n", "(m::real) = n"];
+val simprocs = [hd(rev real_cancel_numeral_factors)];
fun cvar(th,_ $ (_ $ _ $ var)) = cterm_of (#sign(rep_thm th)) var;
@@ -57,63 +24,16 @@
in
-val fast_real_arith_simproc = mk_simproc
- "fast_real_arith" real_arith_simproc_pats Fast_Arith.lin_arith_prover;
-
val real_arith_setup =
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} =>
- {add_mono_thms = add_mono_thms @ add_mono_thms_real,
+ {add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms @ real_mult_mono_thms,
- inj_thms = inj_thms, (*FIXME: add real*)
- lessD = lessD, (*We don't change LA_Data_Ref.lessD because the real ordering is dense!*)
- simpset = simpset addsimps (True_implies_equals :: add_rules @ simps)
- addsimprocs simprocs
- addcongs [if_weak_cong]}),
- arith_discrete ("RealDef.real",false),
- Simplifier.change_simpset_of (op addsimprocs) [fast_real_arith_simproc]];
+ inj_thms = inj_thms,
+ lessD = lessD,
+ simpset = simpset addsimps simps addsimprocs simprocs})];
end;
-
-(* Some test data [omitting examples that assume the ordering to be discrete!]
-Goal "!!a::real. [| a <= b; c <= d; x+y<z |] ==> a+c <= b+d";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a <= b; b+b <= c |] ==> a+a <= c";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b <= i+j; a<=b; i<=j |] ==> a+a <= j+j";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. a+b+c <= i+j+k & a<=b & b<=c & i<=j & j<=k --> a+a+a <= k+k+k";
-by (arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \
-\ ==> a <= l";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \
-\ ==> a+a+a+a <= l+l+l+l";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \
-\ ==> a+a+a+a+a <= l+l+l+l+i";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \
-\ ==> a+a+a+a+a+a <= l+l+l+l+i+l";
-by (fast_arith_tac 1);
-qed "";
-
-Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \
-\ ==> #6*a <= #5*l+i";
-by (fast_arith_tac 1);
-qed "";
+(*
+Procedure "assoc_fold" needed?
*)