author | nipkow |
Mon, 18 Dec 2000 14:59:05 +0100 | |
changeset 10693 | 9e4a0e84d0d6 |
parent 10574 | 8f98f0301d67 |
child 10722 | 55c8367bab05 |
permissions | -rw-r--r-- |
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(* Title: HOL/Real/real_arith.ML |
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ID: $Id$ |
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Author: Tobias Nipkow, TU Muenchen |
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Copyright 1999 TU Muenchen |
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Instantiation of the generic linear arithmetic package for type real. |
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*) |
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local |
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(* reduce contradictory <= to False *) |
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val simps = [order_less_irrefl, zero_eq_numeral_0, one_eq_numeral_1, |
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add_real_number_of, minus_real_number_of, diff_real_number_of, |
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mult_real_number_of, eq_real_number_of, less_real_number_of, |
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le_real_number_of_eq_not_less, real_diff_def, |
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real_minus_add_distrib, real_minus_minus]; |
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val add_rules = |
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map rename_numerals |
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[real_add_zero_left, real_add_zero_right, |
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real_add_minus, real_add_minus_left, |
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real_mult_0, real_mult_0_right, |
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real_mult_1, real_mult_1_right, |
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real_mult_minus_1, real_mult_minus_1_right]; |
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val simprocs = [Real_Times_Assoc.conv, Real_Numeral_Simprocs.combine_numerals]@ |
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Real_Numeral_Simprocs.cancel_numerals(* @ real_cancel_numeral_factors*); |
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val mono_ss = simpset() addsimps |
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[real_add_le_mono,real_add_less_mono, |
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real_add_less_le_mono,real_add_le_less_mono]; |
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val add_mono_thms_real = |
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map (fn s => prove_goal (the_context ()) s |
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(fn prems => [cut_facts_tac prems 1, asm_simp_tac mono_ss 1])) |
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["(i <= j) & (k <= l) ==> i + k <= j + (l::real)", |
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"(i = j) & (k <= l) ==> i + k <= j + (l::real)", |
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"(i <= j) & (k = l) ==> i + k <= j + (l::real)", |
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"(i = j) & (k = l) ==> i + k = j + (l::real)", |
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"(i < j) & (k = l) ==> i + k < j + (l::real)", |
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"(i = j) & (k < l) ==> i + k < j + (l::real)", |
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"(i < j) & (k <= l) ==> i + k < j + (l::real)", |
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"(i <= j) & (k < l) ==> i + k < j + (l::real)", |
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"(i < j) & (k < l) ==> i + k < j + (l::real)"]; |
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val real_arith_simproc_pats = |
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map (fn s => Thm.read_cterm (Theory.sign_of (the_context ())) (s, HOLogic.boolT)) |
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["(m::real) < n","(m::real) <= n", "(m::real) = n"]; |
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fun cvar(th,_ $ (_ $ _ $ var)) = cterm_of (#sign(rep_thm th)) var; |
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val real_mult_mono_thms = |
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[(rotate_prems 1 real_mult_less_mono2, |
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cvar(real_mult_less_mono2, hd(prems_of real_mult_less_mono2))), |
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(real_mult_le_mono2, |
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cvar(real_mult_le_mono2, hd(tl(prems_of real_mult_le_mono2))))] |
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in |
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val fast_real_arith_simproc = mk_simproc |
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"fast_real_arith" real_arith_simproc_pats Fast_Arith.lin_arith_prover; |
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val real_arith_setup = |
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[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} => |
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{add_mono_thms = add_mono_thms @ add_mono_thms_real, |
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mult_mono_thms = mult_mono_thms @ real_mult_mono_thms, |
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inj_thms = inj_thms, (*FIXME: add real*) |
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lessD = lessD, (*We don't change LA_Data_Ref.lessD because the real ordering is dense!*) |
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simpset = simpset addsimps (True_implies_equals :: add_rules @ simps) |
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addsimprocs simprocs |
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addcongs [if_weak_cong]}), |
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arith_discrete ("RealDef.real",false), |
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Simplifier.change_simpset_of (op addsimprocs) [fast_real_arith_simproc]]; |
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end; |
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(* Some test data [omitting examples that assume the ordering to be discrete!] |
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Goal "!!a::real. [| a <= b; c <= d; x+y<z |] ==> a+c <= b+d"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a <= b; b+b <= c |] ==> a+a <= c"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b <= i+j; a<=b; i<=j |] ==> a+a <= j+j"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. a+b+c <= i+j+k & a<=b & b<=c & i<=j & j<=k --> a+a+a <= k+k+k"; |
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by (arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
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\ ==> a <= l"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
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\ ==> a+a+a+a <= l+l+l+l"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
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\ ==> a+a+a+a+a <= l+l+l+l+i"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
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\ ==> a+a+a+a+a+a <= l+l+l+l+i+l"; |
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by (fast_arith_tac 1); |
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qed ""; |
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Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
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\ ==> #6*a <= #5*l+i"; |
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by (fast_arith_tac 1); |
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qed ""; |
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*) |