author | paulson |
Thu, 21 Dec 2000 10:11:10 +0100 | |
changeset 10713 | 69c9fc1d11f2 |
parent 10693 | 9e4a0e84d0d6 |
child 10719 | 8666477dd9a2 |
permissions | -rw-r--r-- |
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(* 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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Simprocs and decision procedure for linear arithmetic. |
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*) |
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(*** Simprocs for numeric literals ***) |
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(** Combining of literal coefficients in sums of products **) |
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Goal "(x < y) = (x-y < (#0::int))"; |
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by (simp_tac (simpset() addsimps zcompare_rls) 1); |
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qed "zless_iff_zdiff_zless_0"; |
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Goal "(x = y) = (x-y = (#0::int))"; |
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by (simp_tac (simpset() addsimps zcompare_rls) 1); |
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qed "eq_iff_zdiff_eq_0"; |
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Goal "(x <= y) = (x-y <= (#0::int))"; |
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by (simp_tac (simpset() addsimps zcompare_rls) 1); |
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qed "zle_iff_zdiff_zle_0"; |
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(** For combine_numerals **) |
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Goal "i*u + (j*u + k) = (i+j)*u + (k::int)"; |
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by (asm_simp_tac (simpset() addsimps [zadd_zmult_distrib]) 1); |
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qed "left_zadd_zmult_distrib"; |
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(** For cancel_numerals **) |
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val rel_iff_rel_0_rls = map (inst "y" "?u+?v") |
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[zless_iff_zdiff_zless_0, eq_iff_zdiff_eq_0, |
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zle_iff_zdiff_zle_0] @ |
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map (inst "y" "n") |
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[zless_iff_zdiff_zless_0, eq_iff_zdiff_eq_0, |
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zle_iff_zdiff_zle_0]; |
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Goal "!!i::int. (i*u + m = j*u + n) = ((i-j)*u + m = n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib]@ |
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zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "eq_add_iff1"; |
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Goal "!!i::int. (i*u + m = j*u + n) = (m = (j-i)*u + n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib]@ |
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zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "eq_add_iff2"; |
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Goal "!!i::int. (i*u + m < j*u + n) = ((i-j)*u + m < n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib]@ |
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zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "less_add_iff1"; |
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Goal "!!i::int. (i*u + m < j*u + n) = (m < (j-i)*u + n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib]@ |
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zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "less_add_iff2"; |
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Goal "!!i::int. (i*u + m <= j*u + n) = ((i-j)*u + m <= n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib]@ |
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zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "le_add_iff1"; |
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Goal "!!i::int. (i*u + m <= j*u + n) = (m <= (j-i)*u + n)"; |
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by (asm_simp_tac (simpset() addsimps [zdiff_def, zadd_zmult_distrib] |
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@zadd_ac@rel_iff_rel_0_rls) 1); |
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qed "le_add_iff2"; |
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(*To tidy up the result of a simproc. Only the RHS will be simplified.*) |
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Goal "u = u' ==> (t==u) == (t==u')"; |
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by Auto_tac; |
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qed "eq_cong2"; |
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structure Int_Numeral_Simprocs = |
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struct |
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(*Utilities*) |
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|
10693 | 82 |
fun mk_numeral n = HOLogic.number_of_const HOLogic.intT $ HOLogic.mk_bin n; |
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(*Decodes a binary INTEGER*) |
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fun dest_numeral (Const("Numeral.number_of", _) $ w) = |
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(NumeralSyntax.dest_bin w |
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handle Match => 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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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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val zero = mk_numeral 0; |
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val mk_plus = HOLogic.mk_binop "op +"; |
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val uminus_const = Const ("uminus", HOLogic.intT --> HOLogic.intT); |
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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 [] = zero |
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| mk_sum [t,u] = mk_plus (t, u) |
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| mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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(*this version ALWAYS includes a trailing zero*) |
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fun long_mk_sum [] = zero |
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| long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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val dest_plus = HOLogic.dest_bin "op +" HOLogic.intT; |
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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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113 |
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 uminus_const$t :: ts; |
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fun dest_sum t = dest_summing (true, t, []); |
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|
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121 |
val mk_diff = HOLogic.mk_binop "op -"; |
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122 |
val dest_diff = HOLogic.dest_bin "op -" HOLogic.intT; |
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124 |
val one = mk_numeral 1; |
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val mk_times = HOLogic.mk_binop "op *"; |
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127 |
fun mk_prod [] = one |
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128 |
| mk_prod [t] = t |
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129 |
| mk_prod (t :: ts) = if t = one then mk_prod ts |
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130 |
else mk_times (t, mk_prod ts); |
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|
131 |
|
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|
132 |
val dest_times = HOLogic.dest_bin "op *" HOLogic.intT; |
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|
133 |
|
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|
134 |
fun dest_prod t = |
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|
135 |
let val (t,u) = dest_times t |
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|
136 |
in dest_prod t @ dest_prod u end |
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|
137 |
handle TERM _ => [t]; |
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|
138 |
|
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|
139 |
(*DON'T do the obvious simplifications; that would create special cases*) |
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|
140 |
fun mk_coeff (k, ts) = mk_times (mk_numeral k, ts); |
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|
141 |
|
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|
142 |
(*Express t as a product of (possibly) a numeral with other sorted terms*) |
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|
143 |
fun dest_coeff sign (Const ("uminus", _) $ t) = dest_coeff (~sign) t |
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|
144 |
| dest_coeff sign t = |
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|
145 |
let val ts = sort Term.term_ord (dest_prod t) |
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|
146 |
val (n, ts') = find_first_numeral [] ts |
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|
147 |
handle TERM _ => (1, ts) |
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|
148 |
in (sign*n, mk_prod ts') end; |
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|
149 |
|
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|
150 |
(*Find first coefficient-term THAT MATCHES u*) |
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|
151 |
fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
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|
152 |
| find_first_coeff past u (t::terms) = |
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|
153 |
let val (n,u') = dest_coeff 1 t |
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|
154 |
in if u aconv u' then (n, rev past @ terms) |
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|
155 |
else find_first_coeff (t::past) u terms |
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|
156 |
end |
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|
157 |
handle TERM _ => find_first_coeff (t::past) u terms; |
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|
158 |
|
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|
159 |
|
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|
160 |
(*Simplify #1*n and n*#1 to n*) |
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|
161 |
val add_0s = [zadd_0, zadd_0_right]; |
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|
162 |
val mult_1s = [zmult_1, zmult_1_right, zmult_minus1, zmult_minus1_right]; |
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|
163 |
|
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|
164 |
(*To perform binary arithmetic*) |
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|
165 |
val bin_simps = [add_number_of_left] @ bin_arith_simps @ bin_rel_simps; |
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|
166 |
|
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|
167 |
(*To evaluate binary negations of coefficients*) |
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|
168 |
val zminus_simps = NCons_simps @ |
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|
169 |
[number_of_minus RS sym, |
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|
170 |
bin_minus_1, bin_minus_0, bin_minus_Pls, bin_minus_Min, |
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|
171 |
bin_pred_1, bin_pred_0, bin_pred_Pls, bin_pred_Min]; |
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|
172 |
|
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|
173 |
(*To let us treat subtraction as addition*) |
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|
174 |
val diff_simps = [zdiff_def, zminus_zadd_distrib, zminus_zminus]; |
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|
175 |
|
10713
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176 |
(*push the unary minus down: - x * y = x * - y *) |
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177 |
val int_minus_mult_eq_1_to_2 = |
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178 |
[zmult_zminus, zmult_zminus_right RS sym] MRS trans |> standard; |
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179 |
|
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|
180 |
(*to extract again any uncancelled minuses*) |
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181 |
val int_minus_from_mult_simps = |
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182 |
[zminus_zminus, zmult_zminus, zmult_zminus_right]; |
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|
183 |
|
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|
184 |
(*combine unary minus with numeric literals, however nested within a product*) |
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|
185 |
val int_mult_minus_simps = |
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|
186 |
[zmult_assoc, zmult_zminus RS sym, int_minus_mult_eq_1_to_2]; |
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187 |
|
9436
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|
188 |
(*Apply the given rewrite (if present) just once*) |
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|
189 |
fun trans_tac None = all_tac |
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|
190 |
| trans_tac (Some th) = ALLGOALS (rtac (th RS trans)); |
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|
191 |
|
9544
f9202e219a29
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|
192 |
fun prove_conv name tacs sg (hyps: thm list) (t,u) = |
9436
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|
193 |
if t aconv u then None |
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|
194 |
else |
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|
195 |
let val ct = cterm_of sg (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u))) |
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|
196 |
in Some |
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|
197 |
(prove_goalw_cterm [] ct (K tacs) |
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|
198 |
handle ERROR => error |
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|
199 |
("The error(s) above occurred while trying to prove " ^ |
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|
200 |
string_of_cterm ct ^ "\nInternal failure of simproc " ^ name)) |
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|
201 |
end; |
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|
202 |
|
9544
f9202e219a29
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|
203 |
(*version without the hyps argument*) |
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|
204 |
fun prove_conv_nohyps name tacs sg = prove_conv name tacs sg []; |
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|
205 |
|
9436
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|
206 |
fun simplify_meta_eq rules = |
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|
207 |
mk_meta_eq o |
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|
208 |
simplify (HOL_basic_ss addeqcongs[eq_cong2] addsimps rules) |
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|
209 |
|
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|
210 |
fun prep_simproc (name, pats, proc) = Simplifier.mk_simproc name pats proc; |
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|
211 |
fun prep_pat s = Thm.read_cterm (Theory.sign_of (the_context())) (s, HOLogic.termT); |
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|
212 |
val prep_pats = map prep_pat; |
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|
213 |
|
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|
214 |
structure CancelNumeralsCommon = |
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|
215 |
struct |
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|
216 |
val mk_sum = mk_sum |
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|
217 |
val dest_sum = dest_sum |
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|
218 |
val mk_coeff = mk_coeff |
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|
219 |
val dest_coeff = dest_coeff 1 |
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|
220 |
val find_first_coeff = find_first_coeff [] |
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|
221 |
val trans_tac = trans_tac |
10713
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|
222 |
val norm_tac = |
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|
223 |
ALLGOALS (simp_tac (HOL_ss addsimps add_0s@mult_1s@diff_simps@ |
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|
224 |
zminus_simps@zadd_ac)) |
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|
225 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps bin_simps@int_mult_minus_simps)) |
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|
226 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps int_minus_from_mult_simps@ |
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|
227 |
zadd_ac@zmult_ac)) |
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|
228 |
val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
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|
229 |
val simplify_meta_eq = simplify_meta_eq (add_0s@mult_1s) |
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|
230 |
end; |
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|
231 |
|
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|
232 |
|
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|
233 |
structure EqCancelNumerals = CancelNumeralsFun |
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|
234 |
(open CancelNumeralsCommon |
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|
235 |
val prove_conv = prove_conv "inteq_cancel_numerals" |
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|
236 |
val mk_bal = HOLogic.mk_eq |
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|
237 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.intT |
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|
238 |
val bal_add1 = eq_add_iff1 RS trans |
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changeset
|
239 |
val bal_add2 = eq_add_iff2 RS trans |
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|
240 |
); |
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|
241 |
|
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|
242 |
structure LessCancelNumerals = CancelNumeralsFun |
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|
243 |
(open CancelNumeralsCommon |
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|
244 |
val prove_conv = prove_conv "intless_cancel_numerals" |
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|
245 |
val mk_bal = HOLogic.mk_binrel "op <" |
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parents:
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|
246 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.intT |
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|
247 |
val bal_add1 = less_add_iff1 RS trans |
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parents:
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|
248 |
val bal_add2 = less_add_iff2 RS trans |
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|
249 |
); |
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|
250 |
|
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|
251 |
structure LeCancelNumerals = CancelNumeralsFun |
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|
252 |
(open CancelNumeralsCommon |
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|
253 |
val prove_conv = prove_conv "intle_cancel_numerals" |
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parents:
diff
changeset
|
254 |
val mk_bal = HOLogic.mk_binrel "op <=" |
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parents:
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changeset
|
255 |
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.intT |
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parents:
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changeset
|
256 |
val bal_add1 = le_add_iff1 RS trans |
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parents:
diff
changeset
|
257 |
val bal_add2 = le_add_iff2 RS trans |
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parents:
diff
changeset
|
258 |
); |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
259 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
260 |
val cancel_numerals = |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
261 |
map prep_simproc |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
262 |
[("inteq_cancel_numerals", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
263 |
prep_pats ["(l::int) + m = n", "(l::int) = m + n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
264 |
"(l::int) - m = n", "(l::int) = m - n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
265 |
"(l::int) * m = n", "(l::int) = m * n"], |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
266 |
EqCancelNumerals.proc), |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
267 |
("intless_cancel_numerals", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
268 |
prep_pats ["(l::int) + m < n", "(l::int) < m + n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
269 |
"(l::int) - m < n", "(l::int) < m - n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
270 |
"(l::int) * m < n", "(l::int) < m * n"], |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
271 |
LessCancelNumerals.proc), |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
272 |
("intle_cancel_numerals", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
273 |
prep_pats ["(l::int) + m <= n", "(l::int) <= m + n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
274 |
"(l::int) - m <= n", "(l::int) <= m - n", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
275 |
"(l::int) * m <= n", "(l::int) <= m * n"], |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
276 |
LeCancelNumerals.proc)]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
277 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
278 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
279 |
structure CombineNumeralsData = |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
280 |
struct |
9571 | 281 |
val add = op + : int*int -> int |
9436
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
282 |
val mk_sum = long_mk_sum (*to work for e.g. #2*x + #3*x *) |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
283 |
val dest_sum = dest_sum |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
284 |
val mk_coeff = mk_coeff |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
285 |
val dest_coeff = dest_coeff 1 |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
286 |
val left_distrib = left_zadd_zmult_distrib RS trans |
9544
f9202e219a29
added a dummy "thm list" argument to prove_conv for the new interface to
paulson
parents:
9436
diff
changeset
|
287 |
val prove_conv = prove_conv_nohyps "int_combine_numerals" |
9436
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
288 |
val trans_tac = trans_tac |
10713
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
289 |
val norm_tac = |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
290 |
ALLGOALS (simp_tac (HOL_ss addsimps add_0s@mult_1s@diff_simps@ |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
291 |
zminus_simps@zadd_ac)) |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
292 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps bin_simps@int_mult_minus_simps)) |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
293 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps int_minus_from_mult_simps@ |
69c9fc1d11f2
simproc bug fix: negative literals and large terms
paulson
parents:
10693
diff
changeset
|
294 |
zadd_ac@zmult_ac)) |
9436
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
295 |
val numeral_simp_tac = ALLGOALS |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
296 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
297 |
val simplify_meta_eq = simplify_meta_eq (add_0s@mult_1s) |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
298 |
end; |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
299 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
300 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
301 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
302 |
val combine_numerals = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
303 |
prep_simproc ("int_combine_numerals", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
304 |
prep_pats ["(i::int) + j", "(i::int) - j"], |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
305 |
CombineNumerals.proc); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
306 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
307 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
308 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
309 |
Addsimprocs Int_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
310 |
Addsimprocs [Int_Numeral_Simprocs.combine_numerals]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
311 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
312 |
(*The Abel_Cancel simprocs are now obsolete*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
313 |
Delsimprocs [Int_Cancel.sum_conv, Int_Cancel.rel_conv]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
314 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
315 |
(*examples: |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
316 |
print_depth 22; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
317 |
set timing; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
318 |
set trace_simp; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
319 |
fun test s = (Goal s; by (Simp_tac 1)); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
320 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
321 |
test "l + #2 + #2 + #2 + (l + #2) + (oo + #2) = (uu::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
322 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
323 |
test "#2*u = (u::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
324 |
test "(i + j + #12 + (k::int)) - #15 = y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
325 |
test "(i + j + #12 + (k::int)) - #5 = y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
326 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
327 |
test "y - b < (b::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
328 |
test "y - (#3*b + c) < (b::int) - #2*c"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
329 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
330 |
test "(#2*x - (u*v) + y) - v*#3*u = (w::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
331 |
test "(#2*x*u*v + (u*v)*#4 + y) - v*u*#4 = (w::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
332 |
test "(#2*x*u*v + (u*v)*#4 + y) - v*u = (w::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
333 |
test "u*v - (x*u*v + (u*v)*#4 + y) = (w::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
334 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
335 |
test "(i + j + #12 + (k::int)) = u + #15 + y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
336 |
test "(i + j*#2 + #12 + (k::int)) = j + #5 + y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
337 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
338 |
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)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
339 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
340 |
test "a + -(b+c) + b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
341 |
test "a + -(b+c) - b = (d::int)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
342 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
343 |
(*negative numerals*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
344 |
test "(i + j + #-2 + (k::int)) - (u + #5 + y) = zz"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
345 |
test "(i + j + #-3 + (k::int)) < u + #5 + y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
346 |
test "(i + j + #3 + (k::int)) < u + #-6 + y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
347 |
test "(i + j + #-12 + (k::int)) - #15 = y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
348 |
test "(i + j + #12 + (k::int)) - #-15 = y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
349 |
test "(i + j + #-12 + (k::int)) - #-15 = y"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
350 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
351 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
352 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
353 |
(** Constant folding for integer plus and times **) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
354 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
355 |
(*We do not need |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
356 |
structure Nat_Plus_Assoc = Assoc_Fold (Nat_Plus_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
357 |
structure Int_Plus_Assoc = Assoc_Fold (Int_Plus_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
358 |
because combine_numerals does the same thing*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
359 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
360 |
structure Int_Times_Assoc_Data : ASSOC_FOLD_DATA = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
361 |
struct |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
362 |
val ss = HOL_ss |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
363 |
val eq_reflection = eq_reflection |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
364 |
val sg_ref = Sign.self_ref (Theory.sign_of (the_context ())) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
365 |
val T = HOLogic.intT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
366 |
val plus = Const ("op *", [HOLogic.intT,HOLogic.intT] ---> HOLogic.intT); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
367 |
val add_ac = zmult_ac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
368 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
369 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
370 |
structure Int_Times_Assoc = Assoc_Fold (Int_Times_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
371 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
372 |
Addsimprocs [Int_Times_Assoc.conv]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
373 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
374 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
375 |
(** The same for the naturals **) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
376 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
377 |
structure Nat_Times_Assoc_Data : ASSOC_FOLD_DATA = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
378 |
struct |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
379 |
val ss = HOL_ss |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
380 |
val eq_reflection = eq_reflection |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
381 |
val sg_ref = Sign.self_ref (Theory.sign_of (the_context ())) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
382 |
val T = HOLogic.natT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
383 |
val plus = Const ("op *", [HOLogic.natT,HOLogic.natT] ---> HOLogic.natT); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
384 |
val add_ac = mult_ac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
385 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
386 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
387 |
structure Nat_Times_Assoc = Assoc_Fold (Nat_Times_Assoc_Data); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
388 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
389 |
Addsimprocs [Nat_Times_Assoc.conv]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
390 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
391 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
392 |
(*** decision procedure for linear arithmetic ***) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
393 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
394 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
395 |
(* Linear arithmetic *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
396 |
(*---------------------------------------------------------------------------*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
397 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
398 |
(* |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
399 |
Instantiation of the generic linear arithmetic package for int. |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
400 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
401 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
402 |
(* Update parameters of arithmetic prover *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
403 |
local |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
404 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
405 |
(* reduce contradictory <= to False *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
406 |
val add_rules = simp_thms @ bin_arith_simps @ bin_rel_simps @ |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
407 |
[zadd_0, zadd_0_right, zdiff_def, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
408 |
zadd_zminus_inverse, zadd_zminus_inverse2, |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
409 |
zmult_0, zmult_0_right, |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
410 |
zmult_1, zmult_1_right, |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
411 |
zmult_minus1, zmult_minus1_right, |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
412 |
zminus_zadd_distrib, zminus_zminus, |
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
413 |
int_0, zadd_int RS sym, int_Suc]; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
414 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
415 |
val simprocs = [Int_Times_Assoc.conv, Int_Numeral_Simprocs.combine_numerals]@ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
416 |
Int_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
417 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
418 |
val add_mono_thms_int = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
419 |
map (fn s => prove_goal (the_context ()) s |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
420 |
(fn prems => [cut_facts_tac prems 1, |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
421 |
asm_simp_tac (simpset() addsimps [zadd_zle_mono]) 1])) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
422 |
["(i <= j) & (k <= l) ==> i + k <= j + (l::int)", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
423 |
"(i = j) & (k <= l) ==> i + k <= j + (l::int)", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
424 |
"(i <= j) & (k = l) ==> i + k <= j + (l::int)", |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
425 |
"(i = j) & (k = l) ==> i + k = j + (l::int)" |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
426 |
]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
427 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
428 |
in |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
429 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
430 |
val int_arith_setup = |
10693 | 431 |
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} => |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
432 |
{add_mono_thms = add_mono_thms @ add_mono_thms_int, |
10693 | 433 |
mult_mono_thms = mult_mono_thms, |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
434 |
inj_thms = [zle_int RS iffD2,int_int_eq RS iffD2] @ inj_thms, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
435 |
lessD = lessD @ [add1_zle_eq RS iffD2], |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
436 |
simpset = simpset addsimps add_rules |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
437 |
addsimprocs simprocs |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
438 |
addcongs [if_weak_cong]}), |
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
9571
diff
changeset
|
439 |
arith_inj_const ("IntDef.int", HOLogic.natT --> Type("IntDef.int",[])), |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
440 |
arith_discrete ("IntDef.int", true)]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
441 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
442 |
end; |
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 |
let |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
445 |
val int_arith_simproc_pats = |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
446 |
map (fn s => Thm.read_cterm (Theory.sign_of (the_context())) (s, HOLogic.boolT)) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
447 |
["(m::int) < n","(m::int) <= n", "(m::int) = n"]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
448 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
449 |
val fast_int_arith_simproc = mk_simproc |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
450 |
"fast_int_arith" int_arith_simproc_pats Fast_Arith.lin_arith_prover; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
451 |
in |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
452 |
Addsimprocs [fast_int_arith_simproc] |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
453 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
454 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
455 |
(* Some test data |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
456 |
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
|
457 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
458 |
Goal "!!a::int. [| a < b; c < d |] ==> a-d+ #2 <= b+(-c)"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
459 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
460 |
Goal "!!a::int. [| a < b; c < d |] ==> a+c+ #1 < b+d"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
461 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
462 |
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
|
463 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
464 |
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
|
465 |
\ ==> a+a <= j+j"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
466 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
467 |
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
|
468 |
\ ==> a+a - - #-1 < j+j - #3"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
469 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
470 |
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
|
471 |
by (arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
472 |
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
|
473 |
\ ==> a <= l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
474 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
475 |
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
|
476 |
\ ==> a+a+a+a <= l+l+l+l"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
477 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
478 |
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
|
479 |
\ ==> a+a+a+a+a <= l+l+l+l+i"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
480 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
481 |
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
|
482 |
\ ==> 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
|
483 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
484 |
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
|
485 |
\ ==> #6*a <= #5*l+i"; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
486 |
by (fast_arith_tac 1); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
487 |
*) |