src/HOL/IntDef.thy
changeset 23431 25ca91279a9b
parent 23402 6472c689664f
child 23438 dd824e86fa8a
     1.1 --- a/src/HOL/IntDef.thy	Wed Jun 20 05:06:56 2007 +0200
     1.2 +++ b/src/HOL/IntDef.thy	Wed Jun 20 05:18:39 2007 +0200
     1.3 @@ -365,9 +365,6 @@
     1.4  lemma zadd_int_left: "(int m) + (int n + z) = int (m + n) + z"
     1.5  by simp
     1.6  
     1.7 -lemma int_Suc: "int (Suc m) = 1 + (int m)"
     1.8 -by simp
     1.9 -
    1.10  lemma int_Suc0_eq_1: "int (Suc 0) = 1"
    1.11  by simp
    1.12  
    1.13 @@ -506,7 +503,7 @@
    1.14  lemma of_int_mult [simp]: "of_int (w*z) = of_int w * of_int z"
    1.15  apply (cases w, cases z)
    1.16  apply (simp add: compare_rls of_int left_diff_distrib right_diff_distrib
    1.17 -                 mult add_ac)
    1.18 +                 mult add_ac of_nat_mult)
    1.19  done
    1.20  
    1.21  lemma of_int_le_iff [simp]:
    1.22 @@ -645,7 +642,7 @@
    1.23  
    1.24  lemma of_nat_setprod: "of_nat (setprod f A) = (\<Prod>x\<in>A. of_nat(f x))"
    1.25    apply (cases "finite A")
    1.26 -  apply (erule finite_induct, auto)
    1.27 +  apply (erule finite_induct, auto simp add: of_nat_mult)
    1.28    done
    1.29  
    1.30  lemma of_int_setprod: "of_int (setprod f A) = (\<Prod>x\<in>A. of_int(f x))"
    1.31 @@ -712,41 +709,41 @@
    1.32  
    1.33  subsection {* Legacy theorems *}
    1.34  
    1.35 -lemmas zminus_zminus = minus_minus [where 'a=int]
    1.36 +lemmas zminus_zminus = minus_minus [of "?z::int"]
    1.37  lemmas zminus_0 = minus_zero [where 'a=int]
    1.38 -lemmas zminus_zadd_distrib = minus_add_distrib [where 'a=int]
    1.39 -lemmas zadd_commute = add_commute [where 'a=int]
    1.40 -lemmas zadd_assoc = add_assoc [where 'a=int]
    1.41 -lemmas zadd_left_commute = add_left_commute [where 'a=int]
    1.42 +lemmas zminus_zadd_distrib = minus_add_distrib [of "?z::int" "?w"]
    1.43 +lemmas zadd_commute = add_commute [of "?z::int" "?w"]
    1.44 +lemmas zadd_assoc = add_assoc [of "?z1.0::int" "?z2.0" "?z3.0"]
    1.45 +lemmas zadd_left_commute = add_left_commute [of "?x::int" "?y" "?z"]
    1.46  lemmas zadd_ac = zadd_assoc zadd_commute zadd_left_commute
    1.47  lemmas zmult_ac = OrderedGroup.mult_ac
    1.48 -lemmas zadd_0 = OrderedGroup.add_0_left [where 'a=int]
    1.49 -lemmas zadd_0_right = OrderedGroup.add_0_left [where 'a=int]
    1.50 -lemmas zadd_zminus_inverse2 = left_minus [where 'a=int]
    1.51 -lemmas zmult_zminus = mult_minus_left [where 'a=int]
    1.52 -lemmas zmult_commute = mult_commute [where 'a=int]
    1.53 -lemmas zmult_assoc = mult_assoc [where 'a=int]
    1.54 -lemmas zadd_zmult_distrib = left_distrib [where 'a=int]
    1.55 -lemmas zadd_zmult_distrib2 = right_distrib [where 'a=int]
    1.56 -lemmas zdiff_zmult_distrib = left_diff_distrib [where 'a=int]
    1.57 -lemmas zdiff_zmult_distrib2 = right_diff_distrib [where 'a=int]
    1.58 +lemmas zadd_0 = OrderedGroup.add_0_left [of "?z::int"]
    1.59 +lemmas zadd_0_right = OrderedGroup.add_0_left [of "?z::int"]
    1.60 +lemmas zadd_zminus_inverse2 = left_minus [of "?z::int"]
    1.61 +lemmas zmult_zminus = mult_minus_left [of "?z::int" "?w"]
    1.62 +lemmas zmult_commute = mult_commute [of "?z::int" "?w"]
    1.63 +lemmas zmult_assoc = mult_assoc [of "?z1.0::int" "?z2.0" "?z3.0"]
    1.64 +lemmas zadd_zmult_distrib = left_distrib [of "?z1.0::int" "?z2.0" "?w"]
    1.65 +lemmas zadd_zmult_distrib2 = right_distrib [of "?w::int" "?z1.0" "?z2.0"]
    1.66 +lemmas zdiff_zmult_distrib = left_diff_distrib [of "?z1.0::int" "?z2.0" "?w"]
    1.67 +lemmas zdiff_zmult_distrib2 = right_diff_distrib [of "?w::int" "?z1.0" "?z2.0"]
    1.68  
    1.69  lemmas int_distrib =
    1.70    zadd_zmult_distrib zadd_zmult_distrib2
    1.71    zdiff_zmult_distrib zdiff_zmult_distrib2
    1.72  
    1.73 -lemmas zmult_1 = mult_1_left [where 'a=int]
    1.74 -lemmas zmult_1_right = mult_1_right [where 'a=int]
    1.75 +lemmas zmult_1 = mult_1_left [of "?z::int"]
    1.76 +lemmas zmult_1_right = mult_1_right [of "?z::int"]
    1.77  
    1.78 -lemmas zle_refl = order_refl [where 'a=int]
    1.79 +lemmas zle_refl = order_refl [of "?w::int"]
    1.80  lemmas zle_trans = order_trans [where 'a=int and x="?i" and y="?j" and z="?k"]
    1.81 -lemmas zle_anti_sym = order_antisym [where 'a=int]
    1.82 -lemmas zle_linear = linorder_linear [where 'a=int]
    1.83 +lemmas zle_anti_sym = order_antisym [of "?z::int" "?w"]
    1.84 +lemmas zle_linear = linorder_linear [of "?z::int" "?w"]
    1.85  lemmas zless_linear = linorder_less_linear [where 'a = int]
    1.86  
    1.87 -lemmas zadd_left_mono = add_left_mono [where 'a=int]
    1.88 -lemmas zadd_strict_right_mono = add_strict_right_mono [where 'a=int]
    1.89 -lemmas zadd_zless_mono = add_less_le_mono [where 'a=int]
    1.90 +lemmas zadd_left_mono = add_left_mono [of "?i::int" "?j" "?k"]
    1.91 +lemmas zadd_strict_right_mono = add_strict_right_mono [of "?i::int" "?j" "?k"]
    1.92 +lemmas zadd_zless_mono = add_less_le_mono [of "?w'::int" "?w" "?z'" "?z"]
    1.93  
    1.94  lemmas int_0_less_1 = zero_less_one [where 'a=int]
    1.95  lemmas int_0_neq_1 = zero_neq_one [where 'a=int]
    1.96 @@ -756,16 +753,17 @@
    1.97  lemmas zadd_int = of_nat_add [where 'a=int, symmetric]
    1.98  lemmas int_mult = of_nat_mult [where 'a=int]
    1.99  lemmas zmult_int = of_nat_mult [where 'a=int, symmetric]
   1.100 -lemmas int_eq_0_conv = of_nat_eq_0_iff [where 'a=int]
   1.101 +lemmas int_eq_0_conv = of_nat_eq_0_iff [where 'a=int and m="?n"]
   1.102  lemmas zless_int = of_nat_less_iff [where 'a=int]
   1.103 -lemmas int_less_0_conv = of_nat_less_0_iff [where 'a=int]
   1.104 +lemmas int_less_0_conv = of_nat_less_0_iff [where 'a=int and m="?k"]
   1.105  lemmas zero_less_int_conv = of_nat_0_less_iff [where 'a=int]
   1.106  lemmas zle_int = of_nat_le_iff [where 'a=int]
   1.107  lemmas zero_zle_int = of_nat_0_le_iff [where 'a=int]
   1.108 -lemmas int_le_0_conv = of_nat_le_0_iff [where 'a=int]
   1.109 +lemmas int_le_0_conv = of_nat_le_0_iff [where 'a=int and m="?n"]
   1.110  lemmas int_0 = of_nat_0 [where ?'a_1.0=int]
   1.111  lemmas int_1 = of_nat_1 [where 'a=int]
   1.112 -lemmas abs_int_eq = abs_of_nat [where 'a=int]
   1.113 +lemmas int_Suc = of_nat_Suc [where ?'a_1.0=int]
   1.114 +lemmas abs_int_eq = abs_of_nat [where 'a=int and n="?m"]
   1.115  lemmas of_int_int_eq = of_int_of_nat_eq [where 'a=int]
   1.116  lemmas int_setsum = of_nat_setsum [where 'a=int]
   1.117  lemmas int_setprod = of_nat_setprod [where 'a=int]