author | wenzelm |
Wed, 17 Mar 1999 16:53:46 +0100 | |
changeset 6394 | 3d9fd50fcc43 |
parent 5593 | 33bca87deae5 |
child 6717 | 70b251dc7055 |
permissions | -rw-r--r-- |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
1 |
(* Title: HOL/Integ/Int.ML |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
2 |
ID: $Id$ |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
4 |
Copyright 1998 University of Cambridge |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
5 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
6 |
Type "int" is a linear order |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
7 |
*) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
8 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
9 |
Goal "(w<z) = neg(w-z)"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
10 |
by (simp_tac (simpset() addsimps [zless_def]) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
11 |
qed "zless_eq_neg"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
12 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
13 |
Goal "(w=z) = iszero(w-z)"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
14 |
by (simp_tac (simpset() addsimps [iszero_def, zdiff_eq_eq]) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
15 |
qed "eq_eq_iszero"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
16 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
17 |
Goal "(w<=z) = (~ neg(z-w))"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
18 |
by (simp_tac (simpset() addsimps [zle_def, zless_def]) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
19 |
qed "zle_eq_not_neg"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
20 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
21 |
|
5593 | 22 |
(*** Inequality lemmas involving int (Suc m) ***) |
23 |
||
24 |
Goal "(w < z + int (Suc m)) = (w < z + int m | w = z + int m)"; |
|
25 |
by (auto_tac (claset(), |
|
26 |
simpset() addsimps [zless_iff_Suc_zadd, zadd_assoc, zadd_int])); |
|
27 |
by (cut_inst_tac [("m","m")] int_Suc 1); |
|
28 |
by (cut_inst_tac [("m","n")] int_Suc 1); |
|
29 |
by (Asm_full_simp_tac 1); |
|
30 |
by (exhaust_tac "n" 1); |
|
31 |
by Auto_tac; |
|
32 |
by (cut_inst_tac [("m","m")] int_Suc 1); |
|
33 |
by (full_simp_tac (simpset() addsimps zadd_ac) 1); |
|
34 |
by (asm_full_simp_tac (simpset() addsimps [zadd_assoc RS sym]) 1); |
|
35 |
by (auto_tac (claset(), |
|
36 |
simpset() addsimps [zless_iff_Suc_zadd, zadd_assoc, zadd_int])); |
|
37 |
qed "zless_add_int_Suc_eq"; |
|
38 |
||
39 |
||
40 |
Goal "(w + int (Suc m) <= z) = (w + int m < z)"; |
|
41 |
by (simp_tac (simpset() addsimps [zle_def, zless_add_int_Suc_eq]) 1); |
|
42 |
by (auto_tac (claset() addIs [zle_anti_sym] addEs [zless_asym], |
|
43 |
simpset() addsimps [zless_imp_zle, symmetric zle_def])); |
|
44 |
qed "add_int_Suc_zle_eq"; |
|
45 |
||
46 |
||
47 |
(* (w < int (Suc m)) = (w < int m | w = int m) *) |
|
48 |
bind_thm ("less_int_Suc_eq", |
|
49 |
simplify (simpset()) |
|
50 |
(read_instantiate [("z", "int 0")] zless_add_int_Suc_eq)); |
|
51 |
||
52 |
Goal "(w <= int (Suc m)) = (w <= int m | w = int (Suc m))"; |
|
53 |
by (simp_tac (simpset() addsimps [less_int_Suc_eq, order_le_less]) 1); |
|
54 |
qed "le_int_Suc_eq"; |
|
55 |
||
56 |
||
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
57 |
(*** Monotonicity results ***) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
58 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
59 |
Goal "(v+z < w+z) = (v < (w::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
60 |
by (Simp_tac 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
61 |
qed "zadd_right_cancel_zless"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
62 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
63 |
Goal "(z+v < z+w) = (v < (w::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
64 |
by (Simp_tac 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
65 |
qed "zadd_left_cancel_zless"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
66 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
67 |
Addsimps [zadd_right_cancel_zless, zadd_left_cancel_zless]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
68 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
69 |
Goal "(v+z <= w+z) = (v <= (w::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
70 |
by (Simp_tac 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
71 |
qed "zadd_right_cancel_zle"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
72 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
73 |
Goal "(z+v <= z+w) = (v <= (w::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
74 |
by (Simp_tac 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
75 |
qed "zadd_left_cancel_zle"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
76 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
77 |
Addsimps [zadd_right_cancel_zle, zadd_left_cancel_zle]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
78 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
79 |
(*"v<=w ==> v+z <= w+z"*) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
80 |
bind_thm ("zadd_zless_mono1", zadd_right_cancel_zless RS iffD2); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
81 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
82 |
(*"v<=w ==> v+z <= w+z"*) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
83 |
bind_thm ("zadd_zle_mono1", zadd_right_cancel_zle RS iffD2); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
84 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
85 |
Goal "!!z z'::int. [| w'<=w; z'<=z |] ==> w' + z' <= w + z"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
86 |
by (etac (zadd_zle_mono1 RS zle_trans) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
87 |
by (Simp_tac 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
88 |
qed "zadd_zle_mono"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
89 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
90 |
Goal "!!z z'::int. [| w'<w; z'<=z |] ==> w' + z' < w + z"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
91 |
by (etac (zadd_zless_mono1 RS zless_zle_trans) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
92 |
by (Simp_tac 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
93 |
qed "zadd_zless_mono"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
94 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
95 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
96 |
(*** Comparison laws ***) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
97 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
98 |
Goal "(- x < - y) = (y < (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
99 |
by (simp_tac (simpset() addsimps [zless_def, zdiff_def] @ zadd_ac) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
100 |
qed "zminus_zless_zminus"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
101 |
Addsimps [zminus_zless_zminus]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
102 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
103 |
Goal "(- x <= - y) = (y <= (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
104 |
by (simp_tac (simpset() addsimps [zle_def]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
105 |
qed "zminus_zle_zminus"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
106 |
Addsimps [zminus_zle_zminus]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
107 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
108 |
(** The next several equations can make the simplifier loop! **) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
109 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
110 |
Goal "(x < - y) = (y < - (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
111 |
by (simp_tac (simpset() addsimps [zless_def, zdiff_def] @ zadd_ac) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
112 |
qed "zless_zminus"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
113 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
114 |
Goal "(- x < y) = (- y < (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
115 |
by (simp_tac (simpset() addsimps [zless_def, zdiff_def] @ zadd_ac) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
116 |
qed "zminus_zless"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
117 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
118 |
Goal "(x <= - y) = (y <= - (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
119 |
by (simp_tac (simpset() addsimps [zle_def, zminus_zless]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
120 |
qed "zle_zminus"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
121 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
122 |
Goal "(- x <= y) = (- y <= (x::int))"; |
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
123 |
by (simp_tac (simpset() addsimps [zle_def, zless_zminus]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
124 |
qed "zminus_zle"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
125 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
126 |
Goal "- (int (Suc n)) < int 0"; |
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
127 |
by (simp_tac (simpset() addsimps [zless_def]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
128 |
qed "negative_zless_0"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
129 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
130 |
Goal "- (int (Suc n)) < int m"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
131 |
by (rtac (negative_zless_0 RS zless_zle_trans) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
132 |
by (Simp_tac 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
133 |
qed "negative_zless"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
134 |
AddIffs [negative_zless]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
135 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
136 |
Goal "- int n <= int 0"; |
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
137 |
by (simp_tac (simpset() addsimps [zminus_zle]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
138 |
qed "negative_zle_0"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
139 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
140 |
Goal "- int n <= int m"; |
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
141 |
by (simp_tac (simpset() addsimps [zless_def, zle_def, zdiff_def, zadd_int]) 1); |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
142 |
qed "negative_zle"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
143 |
AddIffs [negative_zle]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
144 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
145 |
Goal "~(int 0 <= - (int (Suc n)))"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
146 |
by (stac zle_zminus 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
147 |
by (Simp_tac 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
148 |
qed "not_zle_0_negative"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
149 |
Addsimps [not_zle_0_negative]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
150 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
151 |
Goal "(int n <= - int m) = (n = 0 & m = 0)"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
152 |
by Safe_tac; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
153 |
by (Simp_tac 3); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
154 |
by (dtac (zle_zminus RS iffD1) 2); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
155 |
by (ALLGOALS (dtac (negative_zle_0 RSN(2,zle_trans)))); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
156 |
by (ALLGOALS Asm_full_simp_tac); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
157 |
qed "int_zle_neg"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
158 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
159 |
Goal "~(int n < - int m)"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
160 |
by (simp_tac (simpset() addsimps [symmetric zle_def]) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
161 |
qed "not_int_zless_negative"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
162 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
163 |
Goal "(- int n = int m) = (n = 0 & m = 0)"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
164 |
by (rtac iffI 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
165 |
by (rtac (int_zle_neg RS iffD1) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
166 |
by (dtac sym 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
167 |
by (ALLGOALS Asm_simp_tac); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
168 |
qed "negative_eq_positive"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
169 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
170 |
Addsimps [negative_eq_positive, not_int_zless_negative]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
171 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
172 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
173 |
Goal "(w <= z) = (EX n. z = w + int n)"; |
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
174 |
by (auto_tac (claset() addSIs [not_sym RS not0_implies_Suc], |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
175 |
simpset() addsimps [zless_iff_Suc_zadd, integ_le_less])); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
176 |
qed "zle_iff_zadd"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
177 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
178 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
179 |
Goalw [zdiff_def,zless_def] "neg x = (x < int 0)"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
180 |
by Auto_tac; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
181 |
qed "neg_eq_less_nat0"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
182 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
183 |
Goalw [zle_def] "(~neg x) = (int 0 <= x)"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
184 |
by (simp_tac (simpset() addsimps [neg_eq_less_nat0]) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
185 |
qed "not_neg_eq_ge_nat0"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
186 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
187 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
188 |
(**** nat: magnitide of an integer, as a natural number ****) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
189 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
190 |
Goalw [nat_def] "nat(int n) = n"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
191 |
by Auto_tac; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
192 |
qed "nat_nat"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
193 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
194 |
Goalw [nat_def] "nat(- int n) = 0"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
195 |
by (auto_tac (claset(), |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
196 |
simpset() addsimps [neg_eq_less_nat0, zminus_zless])); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
197 |
qed "nat_zminus_nat"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
198 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
199 |
Addsimps [nat_nat, nat_zminus_nat]; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
200 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
201 |
Goal "~ neg z ==> int (nat z) = z"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
202 |
by (dtac (not_neg_eq_ge_nat0 RS iffD1) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
203 |
by (dtac zle_imp_zless_or_eq 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
204 |
by (auto_tac (claset(), simpset() addsimps [zless_iff_Suc_zadd])); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
205 |
qed "not_neg_nat"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
206 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
207 |
Goal "neg x ==> ? n. x = - (int (Suc n))"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
208 |
by (auto_tac (claset(), |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
209 |
simpset() addsimps [neg_eq_less_nat0, zless_iff_Suc_zadd, |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
210 |
zdiff_eq_eq RS sym, zdiff_def])); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
211 |
qed "negD"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
212 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
213 |
Goalw [nat_def] "neg z ==> nat z = 0"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
214 |
by Auto_tac; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
215 |
qed "neg_nat"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
216 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
217 |
(* a case theorem distinguishing positive and negative int *) |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
218 |
|
5582
a356fb49e69e
many renamings and changes. Simproc for cancelling common terms in relations
paulson
parents:
5562
diff
changeset
|
219 |
val prems = Goal "[|!! n. P (int n); !! n. P (- (int (Suc n))) |] ==> P z"; |
5562
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
220 |
by (case_tac "neg z" 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
221 |
by (blast_tac (claset() addSDs [negD] addSIs prems) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
222 |
by (etac (not_neg_nat RS subst) 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
223 |
by (resolve_tac prems 1); |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
224 |
qed "int_cases"; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
225 |
|
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
226 |
fun int_case_tac x = res_inst_tac [("z",x)] int_cases; |
02261e6880d1
Renaming of Integ/Integ.* to Integ/Int.*, and renaming of related constants
paulson
parents:
diff
changeset
|
227 |