author | huffman |
Wed, 09 Nov 2011 10:58:08 +0100 | |
changeset 45435 | d660c4b9daa6 |
parent 45285 | 299abd2931d5 |
child 45436 | 62bc9474d04b |
permissions | -rw-r--r-- |
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1 |
(* Title: HOL/ex/Simproc_Tests.thy |
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Author: Brian Huffman |
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3 |
*) |
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|
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add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
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header {* Testing of arithmetic simprocs *} |
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|
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add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
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theory Simproc_Tests |
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8 |
imports Rat |
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9 |
begin |
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|
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add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
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11 |
text {* |
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12 |
This theory tests the various simprocs defined in |
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@{file "~~/src/HOL/Numeral_Simprocs.thy"}. Many of the tests |
b1d5b3820d82
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are derived from commented-out code originally found in |
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@{file "~~/src/HOL/Tools/numeral_simprocs.ML"}. |
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*} |
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|
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18 |
subsection {* ML bindings *} |
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|
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add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
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ML {* |
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fun test ps = CHANGED (asm_simp_tac (HOL_basic_ss addsimprocs ps) 1) |
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*} |
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23 |
|
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|
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subsection {* @{text int_combine_numerals} *} |
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26 |
|
45435
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27 |
notepad begin |
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28 |
fix a b c d oo uu i j k l u v w x y z :: "'a::number_ring" |
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29 |
{ |
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30 |
assume "10 + (2 * l + oo) = uu" |
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31 |
have "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = uu" |
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32 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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33 |
next |
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34 |
assume "-3 + (i + (j + k)) = y" |
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35 |
have "(i + j + 12 + k) - 15 = y" |
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36 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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37 |
next |
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38 |
assume "7 + (i + (j + k)) = y" |
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39 |
have "(i + j + 12 + k) - 5 = y" |
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add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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40 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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41 |
next |
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42 |
assume "-4 * (u * v) + (2 * x + y) = w" |
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43 |
have "(2*x - (u*v) + y) - v*3*u = w" |
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44 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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45 |
next |
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46 |
assume "Numeral0 * (u*v) + (2 * x * u * v + y) = w" |
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47 |
have "(2*x*u*v + (u*v)*4 + y) - v*u*4 = w" |
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48 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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49 |
next |
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50 |
assume "3 * (u * v) + (2 * x * u * v + y) = w" |
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51 |
have "(2*x*u*v + (u*v)*4 + y) - v*u = w" |
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52 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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53 |
next |
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54 |
assume "-3 * (u * v) + (- (x * u * v) + - y) = w" |
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55 |
have "u*v - (x*u*v + (u*v)*4 + y) = w" |
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56 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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57 |
next |
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58 |
assume "Numeral0 * b + (a + - c) = d" |
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59 |
have "a + -(b+c) + b = d" |
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60 |
apply (simp only: minus_add_distrib) |
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61 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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62 |
next |
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63 |
assume "-2 * b + (a + - c) = d" |
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64 |
have "a + -(b+c) - b = d" |
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65 |
apply (simp only: minus_add_distrib) |
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66 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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67 |
next |
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68 |
assume "-7 + (i + (j + (k + (- u + - y)))) = z" |
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69 |
have "(i + j + -2 + k) - (u + 5 + y) = z" |
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|
70 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
71 |
next |
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72 |
assume "-27 + (i + (j + k)) = y" |
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|
73 |
have "(i + j + -12 + k) - 15 = y" |
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add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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parents:
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|
74 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
d660c4b9daa6
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|
75 |
next |
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76 |
assume "27 + (i + (j + k)) = y" |
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parents:
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|
77 |
have "(i + j + 12 + k) - -15 = y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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parents:
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|
78 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
79 |
next |
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|
80 |
assume "3 + (i + (j + k)) = y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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parents:
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changeset
|
81 |
have "(i + j + -12 + k) - -15 = y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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parents:
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|
82 |
by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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83 |
} |
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84 |
end |
45224
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85 |
|
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86 |
subsection {* @{text inteq_cancel_numerals} *} |
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87 |
|
45435
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|
88 |
notepad begin |
d660c4b9daa6
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|
89 |
fix i j k u vv w y z w' y' z' :: "'a::number_ring" |
d660c4b9daa6
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|
90 |
{ |
d660c4b9daa6
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|
91 |
assume "u = Numeral0" have "2*u = u" |
d660c4b9daa6
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|
92 |
by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
45224
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93 |
(* conclusion matches Rings.ring_1_no_zero_divisors_class.mult_cancel_right2 *) |
45435
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|
94 |
next |
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changeset
|
95 |
assume "i + (j + k) = 3 + (u + y)" |
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changeset
|
96 |
have "(i + j + 12 + k) = u + 15 + y" |
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changeset
|
97 |
by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
d660c4b9daa6
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changeset
|
98 |
next |
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changeset
|
99 |
assume "7 + (j + (i + k)) = y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
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parents:
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changeset
|
100 |
have "(i + j*2 + 12 + k) = j + 5 + y" |
d660c4b9daa6
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|
101 |
by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
d660c4b9daa6
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|
102 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
103 |
assume "u + (6*z + (4*y + 6*w)) = 6*z' + (4*y' + (6*w' + vv))" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
104 |
have "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + vv" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
105 |
by (tactic {* test [@{simproc int_combine_numerals}, @{simproc inteq_cancel_numerals}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
106 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
107 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
108 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
109 |
subsection {* @{text intless_cancel_numerals} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
110 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
111 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
112 |
fix b c i j k u y :: "'a::{linordered_idom,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
113 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
114 |
assume "y < 2 * b" have "y - b < b" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
115 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
116 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
117 |
assume "c + y < 4 * b" have "y - (3*b + c) < b - 2*c" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
118 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
119 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
120 |
assume "i + (j + k) < 8 + (u + y)" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
121 |
have "(i + j + -3 + k) < u + 5 + y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
122 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
123 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
124 |
assume "9 + (i + (j + k)) < u + y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
125 |
have "(i + j + 3 + k) < u + -6 + y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
126 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
127 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
128 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
129 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
130 |
subsection {* @{text ring_eq_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
131 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
132 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
133 |
fix x y :: "'a::{idom,ring_char_0,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
134 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
135 |
assume "3*x = 4*y" have "9*x = 12 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
136 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
137 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
138 |
assume "-3*x = 4*y" have "-99*x = 132 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
139 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
140 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
141 |
assume "111*x = -44*y" have "999*x = -396 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
142 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
143 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
144 |
assume "11*x = 9*y" have "-99*x = -81 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
145 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
146 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
147 |
assume "2*x = Numeral1*y" have "-2 * x = -1 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
148 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
149 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
150 |
assume "2*x = Numeral1*y" have "-2 * x = -y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
151 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
152 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
153 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
154 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
155 |
subsection {* @{text int_div_cancel_numeral_factors} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
156 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
157 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
158 |
fix x y z :: "'a::{semiring_div,ring_char_0,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
159 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
160 |
assume "(3*x) div (4*y) = z" have "(9*x) div (12*y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
161 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
162 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
163 |
assume "(-3*x) div (4*y) = z" have "(-99*x) div (132*y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
164 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
165 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
166 |
assume "(111*x) div (-44*y) = z" have "(999*x) div (-396*y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
167 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
168 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
169 |
assume "(11*x) div (9*y) = z" have "(-99*x) div (-81*y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
170 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
171 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
172 |
assume "(2*x) div (Numeral1*y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
173 |
have "(-2 * x) div (-1 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
174 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
175 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
176 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
177 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
178 |
subsection {* @{text ring_less_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
179 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
180 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
181 |
fix x y :: "'a::{linordered_idom,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
182 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
183 |
assume "3*x < 4*y" have "9*x < 12 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
184 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
185 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
186 |
assume "-3*x < 4*y" have "-99*x < 132 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
187 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
188 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
189 |
assume "111*x < -44*y" have "999*x < -396 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
190 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
191 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
192 |
assume "9*y < 11*x" have "-99*x < -81 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
193 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
194 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
195 |
assume "Numeral1*y < 2*x" have "-2 * x < -y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
196 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
197 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
198 |
assume "23*y < Numeral1*x" have "-x < -23 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
199 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
200 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
201 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
202 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
203 |
subsection {* @{text ring_le_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
204 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
205 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
206 |
fix x y :: "'a::{linordered_idom,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
207 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
208 |
assume "3*x \<le> 4*y" have "9*x \<le> 12 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
209 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
210 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
211 |
assume "-3*x \<le> 4*y" have "-99*x \<le> 132 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
212 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
213 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
214 |
assume "111*x \<le> -44*y" have "999*x \<le> -396 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
215 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
216 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
217 |
assume "9*y \<le> 11*x" have "-99*x \<le> -81 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
218 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
219 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
220 |
assume "Numeral1*y \<le> 2*x" have "-2 * x \<le> -1 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
221 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
222 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
223 |
assume "23*y \<le> Numeral1*x" have "-x \<le> -23 * y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
224 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
225 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
226 |
assume "Numeral1*y \<le> Numeral0" have "0 \<le> y * -2" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
227 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
228 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
229 |
assume "-1*x \<le> Numeral1*y" have "- (2 * x) \<le> 2*y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
230 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
231 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
232 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
233 |
|
45285 | 234 |
subsection {* @{text divide_cancel_numeral_factor} *} |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
235 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
236 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
237 |
fix x y z :: "'a::{field_inverse_zero,ring_char_0,number_ring}" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
238 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
239 |
assume "(3*x) / (4*y) = z" have "(9*x) / (12 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
240 |
by (tactic {* test [@{simproc divide_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
241 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
242 |
assume "(-3*x) / (4*y) = z" have "(-99*x) / (132 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
243 |
by (tactic {* test [@{simproc divide_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
244 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
245 |
assume "(111*x) / (-44*y) = z" have "(999*x) / (-396 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
246 |
by (tactic {* test [@{simproc divide_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
247 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
248 |
assume "(11*x) / (9*y) = z" have "(-99*x) / (-81 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
249 |
by (tactic {* test [@{simproc divide_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
250 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
251 |
assume "(2*x) / (Numeral1*y) = z" have "(-2 * x) / (-1 * y) = z" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
252 |
by (tactic {* test [@{simproc divide_cancel_numeral_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
253 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
254 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
255 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
256 |
subsection {* @{text ring_eq_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
257 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
258 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
259 |
fix a b c d k x y :: "'a::idom" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
260 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
261 |
assume "k = 0 \<or> x = y" have "x*k = k*y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
262 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
263 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
264 |
assume "k = 0 \<or> 1 = y" have "k = k*y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
265 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
266 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
267 |
assume "b = 0 \<or> a*c = 1" have "a*(b*c) = b" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
268 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
269 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
270 |
assume "a = 0 \<or> b = 0 \<or> c = d*x" have "a*(b*c) = d*b*(x*a)" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
271 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
272 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
273 |
assume "k = 0 \<or> x = y" have "x*k = k*y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
274 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
275 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
276 |
assume "k = 0 \<or> 1 = y" have "k = k*y" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
277 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
278 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
279 |
end |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
280 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
281 |
subsection {* @{text int_div_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
282 |
|
45435
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
283 |
notepad begin |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
284 |
fix a b c d k uu x y :: "'a::semiring_div" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
285 |
{ |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
286 |
assume "(if k = 0 then 0 else x div y) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
287 |
have "(x*k) div (k*y) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
288 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
289 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
290 |
assume "(if k = 0 then 0 else 1 div y) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
291 |
have "(k) div (k*y) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
292 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
293 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
294 |
assume "(if b = 0 then 0 else a * c) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
295 |
have "(a*(b*c)) div b = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
296 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
297 |
next |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
298 |
assume "(if a = 0 then 0 else if b = 0 then 0 else c div (d * x)) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
299 |
have "(a*(b*c)) div (d*b*(x*a)) = uu" |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
300 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
301 |
} |
d660c4b9daa6
add ring_char_0 class constraints to several simprocs (internal proofs of #n ~= 0 fail for type
huffman
parents:
45285
diff
changeset
|
302 |
end |
45224
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|
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subsection {* @{text divide_cancel_factor} *} |
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|
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306 |
notepad begin |
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fix a b c d k uu x y :: "'a::field_inverse_zero" |
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{ |
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assume "(if k = 0 then 0 else x / y) = uu" |
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have "(x*k) / (k*y) = uu" |
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by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
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next |
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assume "(if k = 0 then 0 else 1 / y) = uu" |
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have "(k) / (k*y) = uu" |
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by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
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316 |
next |
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assume "(if b = 0 then 0 else a * c / 1) = uu" |
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318 |
have "(a*(b*c)) / b = uu" |
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by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
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next |
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assume "(if a = 0 then 0 else if b = 0 then 0 else c / (d * x)) = uu" |
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have "(a*(b*c)) / (d*b*(x*a)) = uu" |
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323 |
by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
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} |
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325 |
end |
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|
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lemma shows "a*(b*c)/(y*z) = d*(b::rat)*(x*a)/z" |
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oops -- "FIXME: need simproc to cover this case" |
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329 |
|
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330 |
|
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331 |
subsection {* @{text linordered_ring_less_cancel_factor} *} |
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|
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333 |
notepad begin |
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fix x y z :: "'a::linordered_idom" |
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{ |
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336 |
assume "0 < z \<Longrightarrow> x < y" have "0 < z \<Longrightarrow> x*z < y*z" |
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by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
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338 |
next |
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assume "0 < z \<Longrightarrow> x < y" have "0 < z \<Longrightarrow> x*z < z*y" |
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by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
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next |
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342 |
assume "0 < z \<Longrightarrow> x < y" have "0 < z \<Longrightarrow> z*x < y*z" |
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343 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
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344 |
next |
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345 |
assume "0 < z \<Longrightarrow> x < y" have "0 < z \<Longrightarrow> z*x < z*y" |
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346 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
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347 |
} |
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348 |
end |
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349 |
|
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350 |
subsection {* @{text linordered_ring_le_cancel_factor} *} |
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|
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352 |
notepad begin |
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353 |
fix x y z :: "'a::linordered_idom" |
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354 |
{ |
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|
355 |
assume "0 < z \<Longrightarrow> x \<le> y" have "0 < z \<Longrightarrow> x*z \<le> y*z" |
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|
356 |
by (tactic {* test [@{simproc linordered_ring_le_cancel_factor}] *}) fact |
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|
357 |
next |
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|
358 |
assume "0 < z \<Longrightarrow> x \<le> y" have "0 < z \<Longrightarrow> z*x \<le> z*y" |
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|
359 |
by (tactic {* test [@{simproc linordered_ring_le_cancel_factor}] *}) fact |
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|
360 |
} |
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|
361 |
end |
45224
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|
362 |
|
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|
363 |
subsection {* @{text field_combine_numerals} *} |
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364 |
|
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|
365 |
notepad begin |
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|
366 |
fix x uu :: "'a::{field_inverse_zero,ring_char_0,number_ring}" |
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|
367 |
{ |
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|
368 |
assume "5 / 6 * x = uu" have "x / 2 + x / 3 = uu" |
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|
369 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
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|
370 |
next |
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changeset
|
371 |
assume "6 / 9 * x + y = uu" have "x / 3 + y + x / 3 = uu" |
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|
372 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
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|
373 |
next |
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|
374 |
assume "9 / 9 * x = uu" have "2 * x / 3 + x / 3 = uu" |
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375 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
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|
376 |
} |
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|
377 |
end |
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changeset
|
378 |
|
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changeset
|
379 |
lemma "2/3 * (x::rat) + x / 3 = uu" |
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use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
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changeset
|
380 |
apply (tactic {* test [@{simproc field_combine_numerals}] *})? |
45224
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changeset
|
381 |
oops -- "FIXME: test fails" |
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changeset
|
382 |
|
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changeset
|
383 |
end |