author | wenzelm |
Thu, 19 Jan 2006 21:22:08 +0100 | |
changeset 18708 | 4b3dadb4fe33 |
parent 18328 | 841261f303a1 |
child 19044 | d4bc0ee9383a |
permissions | -rw-r--r-- |
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1 |
(* Title: HOL/Integ/int_arith1.ML |
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ID: $Id$ |
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Authors: Larry Paulson and Tobias Nipkow |
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|
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Simprocs and decision procedure for linear arithmetic. |
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*) |
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|
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(** Misc ML bindings **) |
9 |
||
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val bin_succ_Pls = thm"bin_succ_Pls"; |
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val bin_succ_Min = thm"bin_succ_Min"; |
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val bin_succ_1 = thm"bin_succ_1"; |
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val bin_succ_0 = thm"bin_succ_0"; |
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||
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val bin_pred_Pls = thm"bin_pred_Pls"; |
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val bin_pred_Min = thm"bin_pred_Min"; |
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val bin_pred_1 = thm"bin_pred_1"; |
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val bin_pred_0 = thm"bin_pred_0"; |
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||
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val bin_minus_Pls = thm"bin_minus_Pls"; |
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val bin_minus_Min = thm"bin_minus_Min"; |
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val bin_minus_1 = thm"bin_minus_1"; |
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val bin_minus_0 = thm"bin_minus_0"; |
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||
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val bin_add_Pls = thm"bin_add_Pls"; |
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val bin_add_Min = thm"bin_add_Min"; |
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val bin_add_BIT_11 = thm"bin_add_BIT_11"; |
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val bin_add_BIT_10 = thm"bin_add_BIT_10"; |
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val bin_add_BIT_0 = thm"bin_add_BIT_0"; |
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val bin_add_Pls_right = thm"bin_add_Pls_right"; |
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val bin_add_Min_right = thm"bin_add_Min_right"; |
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val bin_mult_Pls = thm"bin_mult_Pls"; |
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val bin_mult_Min = thm"bin_mult_Min"; |
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val bin_mult_1 = thm"bin_mult_1"; |
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val bin_mult_0 = thm"bin_mult_0"; |
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|
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val neg_def = thm "neg_def"; |
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val iszero_def = thm "iszero_def"; |
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||
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val number_of_succ = thm"number_of_succ"; |
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val number_of_pred = thm"number_of_pred"; |
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val number_of_minus = thm"number_of_minus"; |
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val number_of_add = thm"number_of_add"; |
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val diff_number_of_eq = thm"diff_number_of_eq"; |
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val number_of_mult = thm"number_of_mult"; |
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val double_number_of_BIT = thm"double_number_of_BIT"; |
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val numeral_0_eq_0 = thm"numeral_0_eq_0"; |
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val numeral_1_eq_1 = thm"numeral_1_eq_1"; |
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val numeral_m1_eq_minus_1 = thm"numeral_m1_eq_minus_1"; |
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val mult_minus1 = thm"mult_minus1"; |
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val mult_minus1_right = thm"mult_minus1_right"; |
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val minus_number_of_mult = thm"minus_number_of_mult"; |
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val zero_less_nat_eq = thm"zero_less_nat_eq"; |
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val eq_number_of_eq = thm"eq_number_of_eq"; |
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val iszero_number_of_Pls = thm"iszero_number_of_Pls"; |
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val nonzero_number_of_Min = thm"nonzero_number_of_Min"; |
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val iszero_number_of_BIT = thm"iszero_number_of_BIT"; |
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val iszero_number_of_0 = thm"iszero_number_of_0"; |
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val iszero_number_of_1 = thm"iszero_number_of_1"; |
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val less_number_of_eq_neg = thm"less_number_of_eq_neg"; |
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val le_number_of_eq = thm"le_number_of_eq"; |
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val not_neg_number_of_Pls = thm"not_neg_number_of_Pls"; |
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val neg_number_of_Min = thm"neg_number_of_Min"; |
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val neg_number_of_BIT = thm"neg_number_of_BIT"; |
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val le_number_of_eq_not_less = thm"le_number_of_eq_not_less"; |
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val abs_number_of = thm"abs_number_of"; |
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val number_of_reorient = thm"number_of_reorient"; |
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val add_number_of_left = thm"add_number_of_left"; |
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val mult_number_of_left = thm"mult_number_of_left"; |
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val add_number_of_diff1 = thm"add_number_of_diff1"; |
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val add_number_of_diff2 = thm"add_number_of_diff2"; |
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val less_iff_diff_less_0 = thm"less_iff_diff_less_0"; |
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val eq_iff_diff_eq_0 = thm"eq_iff_diff_eq_0"; |
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val le_iff_diff_le_0 = thm"le_iff_diff_le_0"; |
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val bin_arith_extra_simps = thms"bin_arith_extra_simps"; |
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val bin_arith_simps = thms"bin_arith_simps"; |
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val bin_rel_simps = thms"bin_rel_simps"; |
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val zless_imp_add1_zle = thm "zless_imp_add1_zle"; |
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val combine_common_factor = thm"combine_common_factor"; |
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val eq_add_iff1 = thm"eq_add_iff1"; |
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val eq_add_iff2 = thm"eq_add_iff2"; |
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val less_add_iff1 = thm"less_add_iff1"; |
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val less_add_iff2 = thm"less_add_iff2"; |
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val le_add_iff1 = thm"le_add_iff1"; |
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val le_add_iff2 = thm"le_add_iff2"; |
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val arith_special = thms"arith_special"; |
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structure Bin_Simprocs = |
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struct |
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fun prove_conv tacs sg (hyps: thm list) xs (t, u) = |
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if t aconv u then NONE |
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else |
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let val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u)) |
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in SOME (Goal.prove sg xs [] eq (K (EVERY tacs))) end |
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|
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fun prove_conv_nohyps tacs sg = prove_conv tacs sg []; |
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fun prove_conv_nohyps_novars tacs sg = prove_conv tacs sg [] []; |
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103 |
|
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fun prep_simproc (name, pats, proc) = |
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Simplifier.simproc (Theory.sign_of (the_context())) name pats proc; |
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106 |
|
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fun is_numeral (Const("Numeral.number_of", _) $ w) = true |
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| is_numeral _ = false |
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|
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fun simplify_meta_eq f_number_of_eq f_eq = |
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mk_meta_eq ([f_eq, f_number_of_eq] MRS trans) |
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|
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(*reorientation simprules using ==, for the following simproc*) |
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val meta_zero_reorient = zero_reorient RS eq_reflection |
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val meta_one_reorient = one_reorient RS eq_reflection |
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val meta_number_of_reorient = number_of_reorient RS eq_reflection |
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|
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(*reorientation simplification procedure: reorients (polymorphic) |
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0 = x, 1 = x, nnn = x provided x isn't 0, 1 or a numeral.*) |
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fun reorient_proc sg _ (_ $ t $ u) = |
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case u of |
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Const("0", _) => NONE |
123 |
| Const("1", _) => NONE |
|
124 |
| Const("Numeral.number_of", _) $ _ => NONE |
|
125 |
| _ => SOME (case t of |
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Const("0", _) => meta_zero_reorient |
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| Const("1", _) => meta_one_reorient |
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| Const("Numeral.number_of", _) $ _ => meta_number_of_reorient) |
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|
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val reorient_simproc = |
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prep_simproc ("reorient_simproc", ["0=x", "1=x", "number_of w = x"], reorient_proc) |
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end; |
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136 |
Addsimps arith_special; |
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Addsimprocs [Bin_Simprocs.reorient_simproc]; |
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|
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structure Int_Numeral_Simprocs = |
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struct |
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|
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(*Maps 0 to Numeral0 and 1 to Numeral1 so that arithmetic in simprocs |
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isn't complicated by the abstract 0 and 1.*) |
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val numeral_syms = [numeral_0_eq_0 RS sym, numeral_1_eq_1 RS sym]; |
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|
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(** New term ordering so that AC-rewriting brings numerals to the front **) |
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|
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(*Order integers by absolute value and then by sign. The standard integer |
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ordering is not well-founded.*) |
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fun num_ord (i,j) = |
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(case IntInf.compare (IntInf.abs i, IntInf.abs j) of |
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EQUAL => int_ord (IntInf.sign i, IntInf.sign j) |
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| ord => ord); |
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|
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(*This resembles Term.term_ord, but it puts binary numerals before other |
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non-atomic terms.*) |
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local open Term |
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in |
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fun numterm_ord (Abs (_, T, t), Abs(_, U, u)) = |
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(case numterm_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
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| numterm_ord |
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(Const("Numeral.number_of", _) $ v, Const("Numeral.number_of", _) $ w) = |
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num_ord (HOLogic.dest_binum v, HOLogic.dest_binum w) |
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| numterm_ord (Const("Numeral.number_of", _) $ _, _) = LESS |
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| numterm_ord (_, Const("Numeral.number_of", _) $ _) = GREATER |
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| numterm_ord (t, u) = |
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(case int_ord (size_of_term t, size_of_term u) of |
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EQUAL => |
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let val (f, ts) = strip_comb t and (g, us) = strip_comb u in |
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(case hd_ord (f, g) of EQUAL => numterms_ord (ts, us) | ord => ord) |
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end |
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| ord => ord) |
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and numterms_ord (ts, us) = list_ord numterm_ord (ts, us) |
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end; |
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|
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fun numtermless tu = (numterm_ord tu = LESS); |
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|
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(*Defined in this file, but perhaps needed only for simprocs of type nat.*) |
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val num_ss = HOL_ss settermless numtermless; |
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|
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|
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(** Utilities **) |
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|
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fun mk_numeral T n = HOLogic.number_of_const T $ HOLogic.mk_bin n; |
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|
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(*Decodes a binary INTEGER*) |
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fun dest_numeral (Const("0", _)) = 0 |
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| dest_numeral (Const("1", _)) = 1 |
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| dest_numeral (Const("Numeral.number_of", _) $ w) = |
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(HOLogic.dest_binum w |
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handle TERM _ => raise TERM("Int_Numeral_Simprocs.dest_numeral:1", [w])) |
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| dest_numeral t = raise TERM("Int_Numeral_Simprocs.dest_numeral:2", [t]); |
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|
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fun find_first_numeral past (t::terms) = |
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((dest_numeral t, rev past @ terms) |
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handle TERM _ => find_first_numeral (t::past) terms) |
|
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| find_first_numeral past [] = raise TERM("find_first_numeral", []); |
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|
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val mk_plus = HOLogic.mk_binop "op +"; |
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|
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fun mk_minus t = |
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let val T = Term.fastype_of t |
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in Const ("uminus", T --> T) $ t |
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end; |
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|
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(*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*) |
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fun mk_sum T [] = mk_numeral T 0 |
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| mk_sum T [t,u] = mk_plus (t, u) |
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| mk_sum T (t :: ts) = mk_plus (t, mk_sum T ts); |
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|
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(*this version ALWAYS includes a trailing zero*) |
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fun long_mk_sum T [] = mk_numeral T 0 |
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| long_mk_sum T (t :: ts) = mk_plus (t, mk_sum T ts); |
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|
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val dest_plus = HOLogic.dest_bin "op +" Term.dummyT; |
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|
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(*decompose additions AND subtractions as a sum*) |
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fun dest_summing (pos, Const ("op +", _) $ t $ u, ts) = |
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dest_summing (pos, t, dest_summing (pos, u, ts)) |
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| dest_summing (pos, Const ("op -", _) $ t $ u, ts) = |
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dest_summing (pos, t, dest_summing (not pos, u, ts)) |
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| dest_summing (pos, t, ts) = |
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if pos then t::ts else mk_minus t :: ts; |
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|
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fun dest_sum t = dest_summing (true, t, []); |
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|
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val mk_diff = HOLogic.mk_binop "op -"; |
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val dest_diff = HOLogic.dest_bin "op -" Term.dummyT; |
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|
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val mk_times = HOLogic.mk_binop "op *"; |
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|
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fun mk_prod T = |
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let val one = mk_numeral T 1 |
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fun mk [] = one |
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| mk [t] = t |
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| mk (t :: ts) = if t = one then mk ts else mk_times (t, mk ts) |
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in mk end; |
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|
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(*This version ALWAYS includes a trailing one*) |
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fun long_mk_prod T [] = mk_numeral T 1 |
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| long_mk_prod T (t :: ts) = mk_times (t, mk_prod T ts); |
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|
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val dest_times = HOLogic.dest_bin "op *" Term.dummyT; |
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fun dest_prod t = |
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let val (t,u) = dest_times t |
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in dest_prod t @ dest_prod u end |
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handle TERM _ => [t]; |
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|
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(*DON'T do the obvious simplifications; that would create special cases*) |
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fun mk_coeff (k, t) = mk_times (mk_numeral (Term.fastype_of t) k, t); |
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|
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(*Express t as a product of (possibly) a numeral with other sorted terms*) |
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fun dest_coeff sign (Const ("uminus", _) $ t) = dest_coeff (~sign) t |
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| dest_coeff sign t = |
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let val ts = sort Term.term_ord (dest_prod t) |
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val (n, ts') = find_first_numeral [] ts |
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handle TERM _ => (1, ts) |
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in (sign*n, mk_prod (Term.fastype_of t) ts') end; |
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|
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(*Find first coefficient-term THAT MATCHES u*) |
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fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
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| find_first_coeff past u (t::terms) = |
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let val (n,u') = dest_coeff 1 t |
266 |
in if u aconv u' then (n, rev past @ terms) |
|
267 |
else find_first_coeff (t::past) u terms |
|
268 |
end |
|
269 |
handle TERM _ => find_first_coeff (t::past) u terms; |
|
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|
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|
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(*Simplify Numeral0+n, n+Numeral0, Numeral1*n, n*Numeral1*) |
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val add_0s = thms "add_0s"; |
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val mult_1s = thms "mult_1s"; |
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|
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(*To perform binary arithmetic. The "left" rewriting handles patterns |
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created by the simprocs, such as 3 * (5 * x). *) |
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val bin_simps = [numeral_0_eq_0 RS sym, numeral_1_eq_1 RS sym, |
13462 | 279 |
add_number_of_left, mult_number_of_left] @ |
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bin_arith_simps @ bin_rel_simps; |
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|
14113 | 282 |
(*Binary arithmetic BUT NOT ADDITION since it may collapse adjacent terms |
283 |
during re-arrangement*) |
|
284 |
val non_add_bin_simps = |
|
285 |
bin_simps \\ [add_number_of_left, number_of_add RS sym]; |
|
286 |
||
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(*To evaluate binary negations of coefficients*) |
15013 | 288 |
val minus_simps = [numeral_m1_eq_minus_1 RS sym, number_of_minus RS sym, |
289 |
bin_minus_1, bin_minus_0, bin_minus_Pls, bin_minus_Min, |
|
290 |
bin_pred_1, bin_pred_0, bin_pred_Pls, bin_pred_Min]; |
|
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|
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(*To let us treat subtraction as addition*) |
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val diff_simps = [diff_minus, minus_add_distrib, minus_minus]; |
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|
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(*push the unary minus down: - x * y = x * - y *) |
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val minus_mult_eq_1_to_2 = |
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[minus_mult_left RS sym, minus_mult_right] MRS trans |> standard; |
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298 |
|
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299 |
(*to extract again any uncancelled minuses*) |
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val minus_from_mult_simps = |
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[minus_minus, minus_mult_left RS sym, minus_mult_right RS sym]; |
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302 |
|
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303 |
(*combine unary minus with numeric literals, however nested within a product*) |
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val mult_minus_simps = |
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[mult_assoc, minus_mult_left, minus_mult_eq_1_to_2]; |
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306 |
|
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(*Apply the given rewrite (if present) just once*) |
15531 | 308 |
fun trans_tac NONE = all_tac |
309 |
| trans_tac (SOME th) = ALLGOALS (rtac (th RS trans)); |
|
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310 |
|
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fun simplify_meta_eq rules = |
312 |
let val ss0 = HOL_basic_ss addeqcongs [eq_cong2] addsimps rules |
|
313 |
in fn ss => simplify (Simplifier.inherit_context ss ss0) o mk_meta_eq end |
|
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|
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structure CancelNumeralsCommon = |
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struct |
13462 | 317 |
val mk_sum = mk_sum |
318 |
val dest_sum = dest_sum |
|
319 |
val mk_coeff = mk_coeff |
|
320 |
val dest_coeff = dest_coeff 1 |
|
321 |
val find_first_coeff = find_first_coeff [] |
|
16973 | 322 |
val trans_tac = fn _ => trans_tac |
18328 | 323 |
|
324 |
val norm_ss1 = num_ss addsimps numeral_syms @ add_0s @ mult_1s @ |
|
325 |
diff_simps @ minus_simps @ add_ac |
|
326 |
val norm_ss2 = num_ss addsimps non_add_bin_simps @ mult_minus_simps |
|
327 |
val norm_ss3 = num_ss addsimps minus_from_mult_simps @ add_ac @ mult_ac |
|
16973 | 328 |
fun norm_tac ss = |
18328 | 329 |
ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1)) |
330 |
THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2)) |
|
331 |
THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3)) |
|
332 |
||
333 |
val numeral_simp_ss = HOL_ss addsimps add_0s @ bin_simps |
|
334 |
fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss)) |
|
16973 | 335 |
val simplify_meta_eq = simplify_meta_eq (add_0s @ mult_1s) |
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336 |
end; |
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|
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338 |
|
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structure EqCancelNumerals = CancelNumeralsFun |
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(open CancelNumeralsCommon |
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val prove_conv = Bin_Simprocs.prove_conv |
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val mk_bal = HOLogic.mk_eq |
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val dest_bal = HOLogic.dest_bin "op =" Term.dummyT |
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val bal_add1 = eq_add_iff1 RS trans |
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345 |
val bal_add2 = eq_add_iff2 RS trans |
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346 |
); |
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|
347 |
|
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|
348 |
structure LessCancelNumerals = CancelNumeralsFun |
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|
349 |
(open CancelNumeralsCommon |
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val prove_conv = Bin_Simprocs.prove_conv |
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|
351 |
val mk_bal = HOLogic.mk_binrel "op <" |
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352 |
val dest_bal = HOLogic.dest_bin "op <" Term.dummyT |
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|
353 |
val bal_add1 = less_add_iff1 RS trans |
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|
354 |
val bal_add2 = less_add_iff2 RS trans |
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|
355 |
); |
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|
356 |
|
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|
357 |
structure LeCancelNumerals = CancelNumeralsFun |
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|
358 |
(open CancelNumeralsCommon |
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|
359 |
val prove_conv = Bin_Simprocs.prove_conv |
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|
360 |
val mk_bal = HOLogic.mk_binrel "op <=" |
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|
361 |
val dest_bal = HOLogic.dest_bin "op <=" Term.dummyT |
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|
362 |
val bal_add1 = le_add_iff1 RS trans |
62bb04ab4b01
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|
363 |
val bal_add2 = le_add_iff2 RS trans |
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|
364 |
); |
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|
365 |
|
13462 | 366 |
val cancel_numerals = |
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|
367 |
map Bin_Simprocs.prep_simproc |
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|
368 |
[("inteq_cancel_numerals", |
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|
369 |
["(l::'a::number_ring) + m = n", |
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|
370 |
"(l::'a::number_ring) = m + n", |
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|
371 |
"(l::'a::number_ring) - m = n", |
e96d5c42c4b0
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|
372 |
"(l::'a::number_ring) = m - n", |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
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|
373 |
"(l::'a::number_ring) * m = n", |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
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|
374 |
"(l::'a::number_ring) = m * n"], |
9436
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parents:
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changeset
|
375 |
EqCancelNumerals.proc), |
13462 | 376 |
("intless_cancel_numerals", |
14738 | 377 |
["(l::'a::{ordered_idom,number_ring}) + m < n", |
378 |
"(l::'a::{ordered_idom,number_ring}) < m + n", |
|
379 |
"(l::'a::{ordered_idom,number_ring}) - m < n", |
|
380 |
"(l::'a::{ordered_idom,number_ring}) < m - n", |
|
381 |
"(l::'a::{ordered_idom,number_ring}) * m < n", |
|
382 |
"(l::'a::{ordered_idom,number_ring}) < m * n"], |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
383 |
LessCancelNumerals.proc), |
13462 | 384 |
("intle_cancel_numerals", |
14738 | 385 |
["(l::'a::{ordered_idom,number_ring}) + m <= n", |
386 |
"(l::'a::{ordered_idom,number_ring}) <= m + n", |
|
387 |
"(l::'a::{ordered_idom,number_ring}) - m <= n", |
|
388 |
"(l::'a::{ordered_idom,number_ring}) <= m - n", |
|
389 |
"(l::'a::{ordered_idom,number_ring}) * m <= n", |
|
390 |
"(l::'a::{ordered_idom,number_ring}) <= m * n"], |
|
9436
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|
391 |
LeCancelNumerals.proc)]; |
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|
392 |
|
62bb04ab4b01
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|
393 |
|
62bb04ab4b01
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|
394 |
structure CombineNumeralsData = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
395 |
struct |
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15921
diff
changeset
|
396 |
val add = IntInf.+ |
13462 | 397 |
val mk_sum = long_mk_sum (*to work for e.g. 2*x + 3*x *) |
398 |
val dest_sum = dest_sum |
|
399 |
val mk_coeff = mk_coeff |
|
400 |
val dest_coeff = dest_coeff 1 |
|
14272
5efbb548107d
Tidying of the integer development; towards removing the
paulson
parents:
14271
diff
changeset
|
401 |
val left_distrib = combine_common_factor RS trans |
13485
acf39e924091
tuned prove_conv (error reporting done within meta_simplifier.ML);
wenzelm
parents:
13462
diff
changeset
|
402 |
val prove_conv = Bin_Simprocs.prove_conv_nohyps |
16973 | 403 |
val trans_tac = fn _ => trans_tac |
18328 | 404 |
|
405 |
val norm_ss1 = num_ss addsimps numeral_syms @ add_0s @ mult_1s @ |
|
406 |
diff_simps @ minus_simps @ add_ac |
|
407 |
val norm_ss2 = num_ss addsimps non_add_bin_simps @ mult_minus_simps |
|
408 |
val norm_ss3 = num_ss addsimps minus_from_mult_simps @ add_ac @ mult_ac |
|
16973 | 409 |
fun norm_tac ss = |
18328 | 410 |
ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1)) |
411 |
THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2)) |
|
412 |
THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3)) |
|
413 |
||
414 |
val numeral_simp_ss = HOL_ss addsimps add_0s @ bin_simps |
|
415 |
fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss)) |
|
16973 | 416 |
val simplify_meta_eq = simplify_meta_eq (add_0s @ mult_1s) |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
417 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
418 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
419 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
13462 | 420 |
|
421 |
val combine_numerals = |
|
422 |
Bin_Simprocs.prep_simproc |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
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diff
changeset
|
423 |
("int_combine_numerals", |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
424 |
["(i::'a::number_ring) + j", "(i::'a::number_ring) - j"], |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
425 |
CombineNumerals.proc); |
9436
62bb04ab4b01
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diff
changeset
|
426 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
427 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
428 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
429 |
Addsimprocs Int_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
430 |
Addsimprocs [Int_Numeral_Simprocs.combine_numerals]; |
62bb04ab4b01
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parents:
diff
changeset
|
431 |
|
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
432 |
(*examples: |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
433 |
print_depth 22; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
434 |
set timing; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
435 |
set trace_simp; |
13462 | 436 |
fun test s = (Goal s, by (Simp_tac 1)); |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
437 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
438 |
test "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = (uu::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
439 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
440 |
test "2*u = (u::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
441 |
test "(i + j + 12 + (k::int)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
442 |
test "(i + j + 12 + (k::int)) - 5 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
443 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
444 |
test "y - b < (b::int)"; |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
445 |
test "y - (3*b + c) < (b::int) - 2*c"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
446 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
447 |
test "(2*x - (u*v) + y) - v*3*u = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
448 |
test "(2*x*u*v + (u*v)*4 + y) - v*u*4 = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
449 |
test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::int)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
450 |
test "u*v - (x*u*v + (u*v)*4 + y) = (w::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
451 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
452 |
test "(i + j + 12 + (k::int)) = u + 15 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
453 |
test "(i + j*2 + 12 + (k::int)) = j + 5 + y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
454 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
455 |
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::int)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
456 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
457 |
test "a + -(b+c) + b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
458 |
test "a + -(b+c) - b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
459 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
460 |
(*negative numerals*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
461 |
test "(i + j + -2 + (k::int)) - (u + 5 + y) = zz"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
462 |
test "(i + j + -3 + (k::int)) < u + 5 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
463 |
test "(i + j + 3 + (k::int)) < u + -6 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
464 |
test "(i + j + -12 + (k::int)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
465 |
test "(i + j + 12 + (k::int)) - -15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
466 |
test "(i + j + -12 + (k::int)) - -15 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
467 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
468 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
469 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
470 |
(** Constant folding for multiplication in semirings **) |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
471 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
472 |
(*We do not need folding for addition: combine_numerals does the same thing*) |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
473 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
474 |
structure Semiring_Times_Assoc_Data : ASSOC_FOLD_DATA = |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
475 |
struct |
13462 | 476 |
val ss = HOL_ss |
477 |
val eq_reflection = eq_reflection |
|
16423 | 478 |
val thy_ref = Theory.self_ref (the_context ()) |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
479 |
val add_ac = mult_ac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
480 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
481 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
482 |
structure Semiring_Times_Assoc = Assoc_Fold (Semiring_Times_Assoc_Data); |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
483 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
484 |
val assoc_fold_simproc = |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
485 |
Bin_Simprocs.prep_simproc |
14738 | 486 |
("semiring_assoc_fold", ["(a::'a::comm_semiring_1_cancel) * b"], |
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
487 |
Semiring_Times_Assoc.proc); |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
488 |
|
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
489 |
Addsimprocs [assoc_fold_simproc]; |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
490 |
|
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
491 |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
492 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
493 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
494 |
(*** decision procedure for linear arithmetic ***) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
495 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
496 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
497 |
(* Linear arithmetic *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
498 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
499 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
500 |
(* |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
501 |
Instantiation of the generic linear arithmetic package for int. |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
502 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
503 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
504 |
(* Update parameters of arithmetic prover *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
505 |
local |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
506 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
507 |
(* reduce contradictory <= to False *) |
13462 | 508 |
val add_rules = |
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
509 |
simp_thms @ bin_arith_simps @ bin_rel_simps @ arith_special @ |
14390 | 510 |
[neg_le_iff_le, numeral_0_eq_0, numeral_1_eq_1, |
14369 | 511 |
minus_zero, diff_minus, left_minus, right_minus, |
512 |
mult_zero_left, mult_zero_right, mult_1, mult_1_right, |
|
513 |
minus_mult_left RS sym, minus_mult_right RS sym, |
|
514 |
minus_add_distrib, minus_minus, mult_assoc, |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
515 |
of_nat_0, of_nat_1, of_nat_Suc, of_nat_add, of_nat_mult, |
16473
b24c820a0b85
moving some generic inequalities from integer arith to nat arith
paulson
parents:
16423
diff
changeset
|
516 |
of_int_0, of_int_1, of_int_add, of_int_mult, int_eq_of_nat]; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
517 |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
518 |
val simprocs = [assoc_fold_simproc, Int_Numeral_Simprocs.combine_numerals]@ |
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
519 |
Int_Numeral_Simprocs.cancel_numerals; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
520 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
521 |
in |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
522 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
523 |
val int_arith_setup = |
18708 | 524 |
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} => |
14368
2763da611ad9
converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents:
14331
diff
changeset
|
525 |
{add_mono_thms = add_mono_thms, |
15184 | 526 |
mult_mono_thms = [mult_strict_left_mono,mult_left_mono] @ mult_mono_thms, |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
527 |
inj_thms = [zle_int RS iffD2,int_int_eq RS iffD2] @ inj_thms, |
14272
5efbb548107d
Tidying of the integer development; towards removing the
paulson
parents:
14271
diff
changeset
|
528 |
lessD = lessD @ [zless_imp_add1_zle], |
15921 | 529 |
neqE = thm "linorder_neqE_int" :: neqE, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
530 |
simpset = simpset addsimps add_rules |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
531 |
addsimprocs simprocs |
18708 | 532 |
addcongs [if_weak_cong]}) #> |
533 |
arith_inj_const ("IntDef.of_nat", HOLogic.natT --> HOLogic.intT) #> |
|
534 |
arith_inj_const ("IntDef.int", HOLogic.natT --> HOLogic.intT) #> |
|
535 |
arith_discrete "IntDef.int"; |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
536 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
537 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
538 |
|
13462 | 539 |
val fast_int_arith_simproc = |
540 |
Simplifier.simproc (Theory.sign_of (the_context())) |
|
14387
e96d5c42c4b0
Polymorphic treatment of binary arithmetic using axclasses
paulson
parents:
14378
diff
changeset
|
541 |
"fast_int_arith" |
14738 | 542 |
["(m::'a::{ordered_idom,number_ring}) < n", |
543 |
"(m::'a::{ordered_idom,number_ring}) <= n", |
|
544 |
"(m::'a::{ordered_idom,number_ring}) = n"] Fast_Arith.lin_arith_prover; |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
545 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
546 |
Addsimprocs [fast_int_arith_simproc] |
13462 | 547 |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
548 |
|
15661
9ef583b08647
reverted renaming of Some/None in comments and strings;
wenzelm
parents:
15531
diff
changeset
|
549 |
(* Some test data |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
550 |
Goal "!!a::int. [| a <= b; c <= d; x+y<z |] ==> a+c <= b+d"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
551 |
by (fast_arith_tac 1); |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
552 |
Goal "!!a::int. [| a < b; c < d |] ==> a-d+ 2 <= b+(-c)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
553 |
by (fast_arith_tac 1); |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11713
diff
changeset
|
554 |
Goal "!!a::int. [| a < b; c < d |] ==> a+c+ 1 < b+d"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
555 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
556 |
Goal "!!a::int. [| a <= b; b+b <= c |] ==> a+a <= c"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
557 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
558 |
Goal "!!a::int. [| a+b <= i+j; a<=b; i<=j |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
559 |
\ ==> a+a <= j+j"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
560 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
561 |
Goal "!!a::int. [| a+b < i+j; a<b; i<j |] \ |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
562 |
\ ==> a+a - - -1 < j+j - 3"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
563 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
564 |
Goal "!!a::int. a+b+c <= i+j+k & a<=b & b<=c & i<=j & j<=k --> a+a+a <= k+k+k"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
565 |
by (arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
566 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
567 |
\ ==> a <= l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
568 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
569 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
570 |
\ ==> a+a+a+a <= l+l+l+l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
571 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
572 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
573 |
\ ==> a+a+a+a+a <= l+l+l+l+i"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
574 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
575 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
576 |
\ ==> a+a+a+a+a+a <= l+l+l+l+i+l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
577 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
578 |
Goal "!!a::int. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
579 |
\ ==> 6*a <= 5*l+i"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
580 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
581 |
*) |