# HG changeset patch # User paulson # Date 1396630705 -3600 # Node ID a14831ac3023790f61bc66cdf9dc71eda2e8ce33 # Parent 36489d77c4840735a168eb43cd049e33819101b1 divide_minus_left divide_minus_right are in field_simps but are not default simprules diff -r 36489d77c484 -r a14831ac3023 src/HOL/Decision_Procs/Approximation.thy --- a/src/HOL/Decision_Procs/Approximation.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Decision_Procs/Approximation.thy Fri Apr 04 17:58:25 2014 +0100 @@ -1466,7 +1466,8 @@ using float_divr_nonpos_pos_upper_bound[OF `real x \ 0` `0 < real (- floor_fl x)`] unfolding less_eq_float_def zero_float.rep_eq . - have "exp x = exp (?num * (x / ?num))" using `real ?num \ 0` by auto + have "exp x = exp (?num * (x / ?num))" using `real ?num \ 0` + by (auto simp: divide_minus_left divide_minus_right) also have "\ = exp (x / ?num) ^ ?num" unfolding exp_real_of_nat_mult .. also have "\ \ exp (float_divr prec x (- floor_fl x)) ^ ?num" unfolding num_eq fl_eq by (rule power_mono, rule exp_le_cancel_iff[THEN iffD2], rule float_divr) auto @@ -1486,15 +1487,16 @@ case False hence "0 \ real ?horner" by auto have div_less_zero: "real (float_divl prec x (- floor_fl x)) \ 0" - using `real (floor_fl x) < 0` `real x \ 0` by (auto intro!: order_trans[OF float_divl] divide_nonpos_neg) - + using `real (floor_fl x) < 0` `real x \ 0` + by (auto simp: field_simps intro!: order_trans[OF float_divl]) have "(?lb_exp_horner (float_divl prec x (- floor_fl x))) ^ ?num \ exp (float_divl prec x (- floor_fl x)) ^ ?num" using `0 \ real ?horner`[unfolded floor_fl_def[symmetric]] bnds_exp_horner[OF div_less_zero, unfolded atLeastAtMost_iff, THEN conjunct1] by (auto intro!: power_mono) also have "\ \ exp (x / ?num) ^ ?num" unfolding num_eq fl_eq using float_divl by (auto intro!: power_mono simp del: uminus_float.rep_eq) also have "\ = exp (?num * (x / ?num))" unfolding exp_real_of_nat_mult .. - also have "\ = exp x" using `real ?num \ 0` by auto + also have "\ = exp x" using `real ?num \ 0` + by (auto simp: field_simps) finally show ?thesis unfolding lb_exp.simps if_not_P[OF `\ 0 < x`] if_P[OF `x < - 1`] int_floor_fl_def Let_def if_not_P[OF False] by auto next @@ -1506,7 +1508,8 @@ have "Float 1 -2 \ exp (x / (- floor_fl x))" unfolding Float_num . hence "real (Float 1 -2) ^ ?num \ exp (x / (- floor_fl x)) ^ ?num" by (auto intro!: power_mono) - also have "\ = exp x" unfolding num_eq fl_eq exp_real_of_nat_mult[symmetric] using `real (floor_fl x) \ 0` by auto + also have "\ = exp x" unfolding num_eq fl_eq exp_real_of_nat_mult[symmetric] + using `real (floor_fl x) \ 0` by (auto simp: field_simps) finally show ?thesis unfolding lb_exp.simps if_not_P[OF `\ 0 < x`] if_P[OF `x < - 1`] int_floor_fl_def Let_def if_P[OF True] real_of_float_power . qed diff -r 36489d77c484 -r a14831ac3023 src/HOL/Decision_Procs/Ferrack.thy --- a/src/HOL/Decision_Procs/Ferrack.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Decision_Procs/Ferrack.thy Fri Apr 04 17:58:25 2014 +0100 @@ -1167,7 +1167,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith hence "real c * x + ?e \ 0" by simp with xz have "?P ?z x (Eq (CN 0 c e))" @@ -1184,7 +1184,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith hence "real c * x + ?e \ 0" by simp with xz have "?P ?z x (NEq (CN 0 c e))" @@ -1201,7 +1201,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Lt (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -1217,7 +1217,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Le (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -1233,7 +1233,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Gt (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -1249,7 +1249,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Ge (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } diff -r 36489d77c484 -r a14831ac3023 src/HOL/Decision_Procs/MIR.thy --- a/src/HOL/Decision_Procs/MIR.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Decision_Procs/MIR.thy Fri Apr 04 17:58:25 2014 +0100 @@ -2068,7 +2068,7 @@ from 3 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (Eq (CN 0 c e))) = ?I x (Eq (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -2085,7 +2085,7 @@ from 4 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (NEq (CN 0 c e))) = ?I x (NEq (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -2102,7 +2102,7 @@ from 5 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (Lt (CN 0 c e))) = ?I x (Lt (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -2118,7 +2118,7 @@ from 6 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (Le (CN 0 c e))) = ?I x (Le (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -2134,7 +2134,7 @@ from 7 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (Gt (CN 0 c e))) = ?I x (Gt (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -2150,7 +2150,7 @@ from 8 have nbe: "numbound0 e" by simp fix y have "\ x < (floor (- (Inum (y#bs) e) / (real c))). ?I x (?M (Ge (CN 0 c e))) = ?I x (Ge (CN 0 c e))" - proof (simp add: less_floor_eq , rule allI, rule impI) + proof (simp add: divide_minus_left less_floor_eq , rule allI, rule impI) fix x :: int assume A: "real x + 1 \ - (Inum (y # bs) e / real c)" hence th1:"real x < - (Inum (y # bs) e / real c)" by simp @@ -4267,7 +4267,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith hence "real c * x + ?e \ 0" by simp with xz have "?P ?z x (Eq (CN 0 c e))" @@ -4284,7 +4284,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith hence "real c * x + ?e \ 0" by simp with xz have "?P ?z x (NEq (CN 0 c e))" @@ -4301,7 +4301,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Lt (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -4317,7 +4317,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Le (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -4333,7 +4333,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Gt (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } @@ -4349,7 +4349,7 @@ {fix x assume xz: "x > ?z" with mult_strict_right_mono [OF xz cp] cp - have "(real c * x > - ?e)" by (simp add: mult_ac) + have "(real c * x > - ?e)" by (simp add: divide_minus_left mult_ac) hence "real c * x + ?e > 0" by arith with xz have "?P ?z x (Ge (CN 0 c e))" using numbound0_I[OF nb, where b="x" and bs="bs" and b'="a"] by simp } diff -r 36489d77c484 -r a14831ac3023 src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy --- a/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy Fri Apr 04 17:58:25 2014 +0100 @@ -2708,7 +2708,7 @@ have "?rhs = Ifm vs (-?s / (2*?d) # bs) (Eq (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (-?s / (2*?d)) + ?r = 0" - by (simp add: r[of "- (Itm vs (x # bs) s / (2 * \d\\<^sub>p\<^bsup>vs\<^esup>))"]) + by (simp add: field_simps r[of "- (Itm vs (x # bs) s / (2 * \d\\<^sub>p\<^bsup>vs\<^esup>))"]) also have "\ \ 2 * ?d * (?a * (-?s / (2*?d)) + ?r) = 0" using d mult_cancel_left[of "2*?d" "(?a * (-?s / (2*?d)) + ?r)" 0] by simp also have "\ \ (- ?a * ?s) * (2*?d / (2*?d)) + 2 * ?d * ?r= 0" @@ -2728,12 +2728,12 @@ have "?rhs = Ifm vs (-?t / (2*?c) # bs) (Eq (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (-?t / (2*?c)) + ?r = 0" - by (simp add: r[of "- (?t/ (2 * ?c))"]) + by (simp add: field_simps r[of "- (?t/ (2 * ?c))"]) also have "\ \ 2 * ?c * (?a * (-?t / (2 * ?c)) + ?r) = 0" using c mult_cancel_left[of "2 * ?c" "(?a * (-?t / (2 * ?c)) + ?r)" 0] by simp also have "\ \ (?a * -?t)* (2 * ?c) / (2 * ?c) + 2 * ?c * ?r= 0" by (simp add: field_simps distrib_left[of "2 * ?c"] del: distrib_left) - also have "\ \ - (?a * ?t) + 2 * ?c * ?r = 0" using c by simp + also have "\ \ - (?a * ?t) + 2 * ?c * ?r = 0" using c by (simp add: field_simps) finally have ?thesis using c d by (simp add: r[of "- (?t/ (2 * ?c))"] msubsteq_def Let_def evaldjf_ex) } @@ -2755,7 +2755,7 @@ by simp also have "\ \ ?a * (- (?d * ?t + ?c* ?s )) + 2 * ?c * ?d * ?r = 0" using nonzero_mult_divide_cancel_left [OF dc] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] msubsteq_def Let_def evaldjf_ex field_simps) @@ -2825,7 +2825,7 @@ have "?rhs = Ifm vs (-?s / (2*?d) # bs) (NEq (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (-?s / (2*?d)) + ?r \ 0" - by (simp add: r[of "- (Itm vs (x # bs) s / (2 * \d\\<^sub>p\<^bsup>vs\<^esup>))"]) + by (simp add: field_simps r[of "- (Itm vs (x # bs) s / (2 * \d\\<^sub>p\<^bsup>vs\<^esup>))"]) also have "\ \ 2*?d * (?a * (-?s / (2*?d)) + ?r) \ 0" using d mult_cancel_left[of "2*?d" "(?a * (-?s / (2*?d)) + ?r)" 0] by simp also have "\ \ (- ?a * ?s) * (2*?d / (2*?d)) + 2*?d*?r\ 0" @@ -2845,13 +2845,13 @@ have "?rhs = Ifm vs (-?t / (2*?c) # bs) (NEq (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (-?t / (2*?c)) + ?r \ 0" - by (simp add: r[of "- (?t/ (2 * ?c))"]) + by (simp add: field_simps r[of "- (?t/ (2 * ?c))"]) also have "\ \ 2*?c * (?a * (-?t / (2*?c)) + ?r) \ 0" using c mult_cancel_left[of "2*?c" "(?a * (-?t / (2*?c)) + ?r)" 0] by simp also have "\ \ (?a * -?t)* (2*?c) / (2*?c) + 2*?c*?r \ 0" by (simp add: field_simps distrib_left[of "2*?c"] del: distrib_left) also have "\ \ - (?a * ?t) + 2*?c*?r \ 0" - using c by simp + using c by (simp add: field_simps) finally have ?thesis using c d by (simp add: r[of "- (?t/ (2*?c))"] msubstneq_def Let_def evaldjf_ex) } @@ -2873,7 +2873,7 @@ by simp also have "\ \ ?a * (- (?d * ?t + ?c* ?s )) + 2*?c*?d*?r \ 0" using nonzero_mult_divide_cancel_left[OF dc] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] @@ -2963,7 +2963,7 @@ by simp also have "\ \ ?a * (- (?d * ?t + ?c* ?s )) + 2*?c*?d*?r < 0" using nonzero_mult_divide_cancel_left[of "2*?c*?d"] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using dc c d nc nd dc' by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -2988,7 +2988,7 @@ by simp also have "\ \ ?a * ((?d * ?t + ?c* ?s )) - 2 * ?c * ?d * ?r < 0" using nonzero_mult_divide_cancel_left[of "2 * ?c * ?d"] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using dc c d nc nd by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3005,14 +3005,14 @@ have "?rhs \ Ifm vs (- ?t / (2 * ?c) # bs) (Lt (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?t / (2 * ?c))+ ?r < 0" - by (simp add: r[of "- (?t / (2 * ?c))"]) + by (simp add: field_simps r[of "- (?t / (2 * ?c))"]) also have "\ \ 2 * ?c * (?a * (- ?t / (2 * ?c))+ ?r) < 0" using c mult_less_cancel_left_disj[of "2 * ?c" "?a* (- ?t / (2*?c))+ ?r" 0] c' c'' order_less_not_sym[OF c''] by simp also have "\ \ - ?a * ?t + 2 * ?c * ?r < 0" using nonzero_mult_divide_cancel_left[OF c'] c - by (simp add: algebra_simps diff_divide_distrib less_le del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib less_le del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?t / (2*?c))"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3029,7 +3029,7 @@ have "?rhs \ Ifm vs (- ?t / (2*?c) # bs) (Lt (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?t / (2*?c))+ ?r < 0" - by (simp add: r[of "- (?t / (2*?c))"]) + by (simp add: field_simps r[of "- (?t / (2*?c))"]) also have "\ \ 2 * ?c * (?a * (- ?t / (2 * ?c))+ ?r) > 0" using c order_less_not_sym[OF c''] less_imp_neq[OF c''] c'' mult_less_cancel_left_disj[of "2 * ?c" 0 "?a* (- ?t / (2*?c))+ ?r"] @@ -3037,7 +3037,7 @@ also have "\ \ ?a*?t - 2*?c *?r < 0" using nonzero_mult_divide_cancel_left[OF c'] c order_less_not_sym[OF c''] less_imp_neq[OF c''] c'' - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?t / (2*?c))"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3054,14 +3054,14 @@ have "?rhs \ Ifm vs (- ?s / (2 * ?d) # bs) (Lt (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?s / (2 * ?d))+ ?r < 0" - by (simp add: r[of "- (?s / (2 * ?d))"]) + by (simp add: field_simps r[of "- (?s / (2 * ?d))"]) also have "\ \ 2 * ?d * (?a * (- ?s / (2 * ?d))+ ?r) < 0" using d mult_less_cancel_left_disj[of "2 * ?d" "?a * (- ?s / (2 * ?d))+ ?r" 0] d' d'' order_less_not_sym[OF d''] by simp also have "\ \ - ?a * ?s+ 2 * ?d * ?r < 0" using nonzero_mult_divide_cancel_left[OF d'] d - by (simp add: algebra_simps diff_divide_distrib less_le del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib less_le del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?s / (2*?d))"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3078,7 +3078,7 @@ have "?rhs \ Ifm vs (- ?s / (2 * ?d) # bs) (Lt (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?s / (2 * ?d)) + ?r < 0" - by (simp add: r[of "- (?s / (2 * ?d))"]) + by (simp add: field_simps r[of "- (?s / (2 * ?d))"]) also have "\ \ 2 * ?d * (?a * (- ?s / (2 * ?d)) + ?r) > 0" using d order_less_not_sym[OF d''] less_imp_neq[OF d''] d'' mult_less_cancel_left_disj[of "2 * ?d" 0 "?a* (- ?s / (2*?d))+ ?r"] @@ -3086,7 +3086,7 @@ also have "\ \ ?a * ?s - 2 * ?d * ?r < 0" using nonzero_mult_divide_cancel_left[OF d'] d order_less_not_sym[OF d''] less_imp_neq[OF d''] d'' - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?s / (2*?d))"] msubstlt_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3177,7 +3177,7 @@ by simp also have "\ \ ?a * (- (?d * ?t + ?c* ?s )) + 2*?c*?d*?r \ 0" using nonzero_mult_divide_cancel_left[of "2*?c*?d"] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using dc c d nc nd dc' by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3202,7 +3202,7 @@ by simp also have "\ \ ?a * ((?d * ?t + ?c* ?s )) - 2 * ?c * ?d * ?r \ 0" using nonzero_mult_divide_cancel_left[of "2 * ?c * ?d"] c d - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using dc c d nc nd by (simp add: r[of "(- (?d * ?t) + - (?c *?s)) / (2 * ?c * ?d)"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3219,14 +3219,14 @@ have "?rhs \ Ifm vs (- ?t / (2 * ?c) # bs) (Le (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?t / (2 * ?c))+ ?r \ 0" - by (simp add: r[of "- (?t / (2 * ?c))"]) + by (simp add: field_simps r[of "- (?t / (2 * ?c))"]) also have "\ \ 2 * ?c * (?a * (- ?t / (2 * ?c))+ ?r) \ 0" using c mult_le_cancel_left[of "2 * ?c" "?a* (- ?t / (2*?c))+ ?r" 0] c' c'' order_less_not_sym[OF c''] by simp also have "\ \ - ?a*?t+ 2*?c *?r \ 0" using nonzero_mult_divide_cancel_left[OF c'] c - by (simp add: algebra_simps diff_divide_distrib less_le del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib less_le del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?t / (2*?c))"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3243,7 +3243,7 @@ have "?rhs \ Ifm vs (- ?t / (2 * ?c) # bs) (Le (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?t / (2*?c))+ ?r \ 0" - by (simp add: r[of "- (?t / (2*?c))"]) + by (simp add: field_simps r[of "- (?t / (2*?c))"]) also have "\ \ 2 * ?c * (?a * (- ?t / (2 * ?c))+ ?r) \ 0" using c order_less_not_sym[OF c''] less_imp_neq[OF c''] c'' mult_le_cancel_left[of "2 * ?c" 0 "?a* (- ?t / (2*?c))+ ?r"] @@ -3251,7 +3251,7 @@ also have "\ \ ?a * ?t - 2 * ?c * ?r \ 0" using nonzero_mult_divide_cancel_left[OF c'] c order_less_not_sym[OF c''] less_imp_neq[OF c''] c'' - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?t / (2*?c))"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3268,14 +3268,14 @@ have "?rhs \ Ifm vs (- ?s / (2 * ?d) # bs) (Le (CNP 0 a r))" by (simp only: th) also have "\ \ ?a * (- ?s / (2 * ?d))+ ?r \ 0" - by (simp add: r[of "- (?s / (2*?d))"]) + by (simp add: field_simps r[of "- (?s / (2*?d))"]) also have "\ \ 2 * ?d * (?a * (- ?s / (2 * ?d)) + ?r) \ 0" using d mult_le_cancel_left[of "2 * ?d" "?a* (- ?s / (2*?d))+ ?r" 0] d' d'' order_less_not_sym[OF d''] by simp also have "\ \ - ?a * ?s + 2 * ?d * ?r \ 0" using nonzero_mult_divide_cancel_left[OF d'] d - by (simp add: algebra_simps diff_divide_distrib less_le del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib less_le del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?s / (2*?d))"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3292,7 +3292,7 @@ have "?rhs \ Ifm vs (- ?s / (2*?d) # bs) (Le (CNP 0 a r))" by (simp only: th) also have "\ \ ?a* (- ?s / (2*?d))+ ?r \ 0" - by (simp add: r[of "- (?s / (2*?d))"]) + by (simp add: field_simps r[of "- (?s / (2*?d))"]) also have "\ \ 2*?d * (?a* (- ?s / (2*?d))+ ?r) \ 0" using d order_less_not_sym[OF d''] less_imp_neq[OF d''] d'' mult_le_cancel_left[of "2 * ?d" 0 "?a* (- ?s / (2*?d))+ ?r"] @@ -3300,7 +3300,7 @@ also have "\ \ ?a * ?s - 2 * ?d * ?r \ 0" using nonzero_mult_divide_cancel_left[OF d'] d order_less_not_sym[OF d''] less_imp_neq[OF d''] d'' - by (simp add: algebra_simps diff_divide_distrib del: distrib_right) + by (simp add: divide_minus_left algebra_simps diff_divide_distrib del: distrib_right) finally have ?thesis using c d nc nd by (simp add: r[of "- (?s / (2*?d))"] msubstle_def Let_def evaldjf_ex field_simps lt polyneg_norm polymul_norm) @@ -3326,10 +3326,10 @@ Ifm vs (((- Itm vs (x#bs) t / Ipoly vs c + - Itm vs (x#bs) s / Ipoly vs d) /2)#bs) p" using lp by (induct p rule: islin.induct) - (auto simp add: tmbound0_I + (auto simp add: tmbound0_I [where b = "(- (Itm vs (x # bs) t / \c\\<^sub>p\<^bsup>vs\<^esup>) - (Itm vs (x # bs) s / \d\\<^sub>p\<^bsup>vs\<^esup>)) / 2" and b' = x and bs = bs and vs = vs] - msubsteq msubstneq msubstlt [OF nc nd] msubstle [OF nc nd]) + msubsteq msubstneq msubstlt [OF nc nd] msubstle [OF nc nd] divide_minus_left) lemma msubst_nb: assumes lp: "islin p" @@ -3767,7 +3767,7 @@ by (auto simp add: msubst2_def lt zero_less_mult_iff mult_less_0_iff) from msubst2[OF lp nn nn2(1), of x bs t] have "\n\\<^sub>p\<^bsup>vs\<^esup> \ 0 \ Ifm vs (- Itm vs (x # bs) t / (\n\\<^sub>p\<^bsup>vs\<^esup> * 2) # bs) p" - using H(2) nn2 by (simp add: mult_minus2_right) + using H(2) nn2 by (simp add: divide_minus_left divide_minus_right mult_minus2_right) } moreover { @@ -3780,7 +3780,7 @@ then have nn: "isnpoly (n *\<^sub>p (C (-2,1)))" "\n *\<^sub>p(C (-2,1)) \\<^sub>p\<^bsup>vs\<^esup> \ 0" using H(2) by (simp_all add: polymul_norm n2) from msubst2[OF lp nn, of x bs t] have "?I (msubst2 p (n *\<^sub>p (C (-2,1))) t)" - using H(2,3) by (simp add: mult_minus2_right) + using H(2,3) by (simp add: divide_minus_left divide_minus_right mult_minus2_right) } ultimately show ?thesis by blast qed @@ -3811,7 +3811,7 @@ from msubst2[OF lp nn nn'(1), of x bs ] H(3) nn' have "\c\\<^sub>p\<^bsup>vs\<^esup> \ 0 \ \d\\<^sub>p\<^bsup>vs\<^esup> \ 0 \ Ifm vs ((- Itm vs (x # bs) t / \c\\<^sub>p\<^bsup>vs\<^esup> + - Itm vs (x # bs) s / \d\\<^sub>p\<^bsup>vs\<^esup>) / 2 # bs) p" - by (simp add: add_divide_distrib diff_divide_distrib mult_minus2_left mult_commute) + by (simp add: divide_minus_left divide_minus_right add_divide_distrib diff_divide_distrib mult_minus2_left mult_commute) } moreover { @@ -3828,7 +3828,7 @@ using H(3,4) by (simp_all add: polymul_norm n2) from msubst2[OF lp nn, of x bs ] H(3,4,5) have "Ifm vs (x#bs) (msubst2 p (C (-2, 1) *\<^sub>p c*\<^sub>p d) (Add (Mul d t) (Mul c s)))" - by (simp add: diff_divide_distrib add_divide_distrib mult_minus2_left mult_commute) + by (simp add: divide_minus_left divide_minus_right diff_divide_distrib add_divide_distrib mult_minus2_left mult_commute) } ultimately show ?thesis by blast qed diff -r 36489d77c484 -r a14831ac3023 src/HOL/Decision_Procs/Rat_Pair.thy --- a/src/HOL/Decision_Procs/Rat_Pair.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Decision_Procs/Rat_Pair.thy Fri Apr 04 17:58:25 2014 +0100 @@ -227,7 +227,7 @@ let ?g = "gcd a b" from a b have g: "?g \ 0"by simp from of_int_div[OF g, where ?'a = 'a] - have ?thesis by (auto simp add: x INum_def normNum_def split_def Let_def) } + have ?thesis by (auto simp: divide_minus_left divide_minus_right x INum_def normNum_def split_def Let_def) } ultimately show ?thesis by blast qed @@ -300,13 +300,13 @@ qed lemma Nneg[simp]: "INum (~\<^sub>N x) = - (INum x ::'a:: field)" - by (simp add: Nneg_def split_def INum_def) + by (simp add: divide_minus_left Nneg_def split_def INum_def) lemma Nsub[simp]: "INum (x -\<^sub>N y) = INum x - (INum y:: 'a :: {field_char_0, field_inverse_zero})" by (simp add: Nsub_def split_def) lemma Ninv[simp]: "INum (Ninv x) = (1::'a :: field_inverse_zero) / (INum x)" - by (simp add: Ninv_def INum_def split_def) + by (simp add: divide_minus_left divide_minus_right Ninv_def INum_def split_def) lemma Ndiv[simp]: "INum (x \
\<^sub>N y) = INum x / (INum y ::'a :: {field_char_0, field_inverse_zero})" by (simp add: Ndiv_def) diff -r 36489d77c484 -r a14831ac3023 src/HOL/Fields.thy --- a/src/HOL/Fields.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Fields.thy Fri Apr 04 17:58:25 2014 +0100 @@ -152,7 +152,7 @@ lemma nonzero_minus_divide_divide: "b \ 0 ==> (-a) / (-b) = a / b" by (simp add: divide_inverse nonzero_inverse_minus_eq) -lemma divide_minus_left: "(-a) / b = - (a / b)" +lemma divide_minus_left [field_simps]: "(-a) / b = - (a / b)" by (simp add: divide_inverse) lemma diff_divide_distrib: "(a - b) / c = a / c - b / c" @@ -408,7 +408,7 @@ "- (a / b) = a / - b" by (simp add: divide_inverse) -lemma divide_minus_right: +lemma divide_minus_right [field_simps]: "a / - b = - (a / b)" by (simp add: divide_inverse) diff -r 36489d77c484 -r a14831ac3023 src/HOL/Library/Float.thy --- a/src/HOL/Library/Float.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Library/Float.thy Fri Apr 04 17:58:25 2014 +0100 @@ -637,7 +637,7 @@ qed thus ?thesis using `\ b dvd a` by simp qed (simp add: ceiling_def real_of_int_minus[symmetric] divide_minus_left[symmetric] - floor_divide_eq_div dvd_neg_div del: divide_minus_left real_of_int_minus) + floor_divide_eq_div dvd_neg_div del: real_of_int_minus) lemma compute_float_up[code]: "float_up p (Float m e) = @@ -1004,7 +1004,7 @@ else (if 0 < y then - (rapprox_posrat prec (nat (-x)) (nat y)) else lapprox_posrat prec (nat (-x)) (nat (-y))))" - by transfer (auto simp: round_up_def round_down_def ceiling_def ac_simps) + by transfer (auto simp: round_up_def divide_minus_left divide_minus_right round_down_def ceiling_def ac_simps) hide_fact (open) compute_lapprox_rat lift_definition rapprox_rat :: "nat \ int \ int \ float" is @@ -1019,7 +1019,7 @@ else (if 0 < y then - (lapprox_posrat prec (nat (-x)) (nat y)) else rapprox_posrat prec (nat (-x)) (nat (-y))))" - by transfer (auto simp: round_up_def round_down_def ceiling_def ac_simps) + by transfer (auto simp: round_up_def round_down_def divide_minus_left divide_minus_right ceiling_def ac_simps) hide_fact (open) compute_rapprox_rat subsection {* Division *} diff -r 36489d77c484 -r a14831ac3023 src/HOL/Library/Formal_Power_Series.thy --- a/src/HOL/Library/Formal_Power_Series.thy Thu Apr 03 23:51:52 2014 +0100 +++ b/src/HOL/Library/Formal_Power_Series.thy Fri Apr 04 17:58:25 2014 +0100 @@ -3635,7 +3635,7 @@ done lemma fps_sin_even: "fps_sin (- c) = - fps_sin c" - by (auto simp add: fps_eq_iff fps_sin_def) + by (auto simp add: divide_minus_left fps_eq_iff fps_sin_def) lemma fps_cos_odd: "fps_cos (- c) = fps_cos c" by (auto simp add: fps_eq_iff fps_cos_def)