author | huffman |
Fri, 28 Oct 2011 11:02:27 +0200 | |
changeset 45284 | ae78a4ffa81d |
parent 45270 | d5b5c9259afd |
child 45285 | 299abd2931d5 |
permissions | -rw-r--r-- |
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(* Title: HOL/ex/Simproc_Tests.thy |
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Author: Brian Huffman |
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*) |
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header {* Testing of arithmetic simprocs *} |
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theory Simproc_Tests |
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imports Rat |
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begin |
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text {* |
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This theory tests the various simprocs defined in |
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@{file "~~/src/HOL/Numeral_Simprocs.thy"}. Many of the tests |
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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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subsection {* ML bindings *} |
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ML {* |
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val [field_eq_cancel_numeral_factor, field_cancel_numeral_factor] |
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= Numeral_Simprocs.field_cancel_numeral_factors |
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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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subsection {* @{text int_combine_numerals} *} |
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lemma assumes "10 + (2 * l + oo) = uu" |
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shows "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = (uu::int)" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "-3 + (i + (j + k)) = y" |
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shows "(i + j + 12 + (k::int)) - 15 = y" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "7 + (i + (j + k)) = y" |
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shows "(i + j + 12 + (k::int)) - 5 = y" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "-4 * (u * v) + (2 * x + y) = w" |
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shows "(2*x - (u*v) + y) - v*3*u = (w::int)" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "Numeral0 * (u*v) + (2 * x * u * v + y) = w" |
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shows "(2*x*u*v + (u*v)*4 + y) - v*u*4 = (w::int)" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "3 * (u * v) + (2 * x * u * v + y) = w" |
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shows "(2*x*u*v + (u*v)*4 + y) - v*u = (w::int)" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "-3 * (u * v) + (- (x * u * v) + - y) = w" |
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shows "u*v - (x*u*v + (u*v)*4 + y) = (w::int)" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "Numeral0 * b + (a + - c) = d" |
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shows "a + -(b+c) + b = (d::int)" |
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apply (simp only: minus_add_distrib) |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "-2 * b + (a + - c) = d" |
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shows "a + -(b+c) - b = (d::int)" |
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apply (simp only: minus_add_distrib) |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "-7 + (i + (j + (k + (- u + - y)))) = zz" |
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shows "(i + j + -2 + (k::int)) - (u + 5 + y) = zz" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "-27 + (i + (j + k)) = y" |
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shows "(i + j + -12 + (k::int)) - 15 = y" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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lemma assumes "27 + (i + (j + k)) = y" |
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shows "(i + j + 12 + (k::int)) - -15 = y" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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lemma assumes "3 + (i + (j + k)) = y" |
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shows "(i + j + -12 + (k::int)) - -15 = y" |
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by (tactic {* test [@{simproc int_combine_numerals}] *}) fact |
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|
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subsection {* @{text inteq_cancel_numerals} *} |
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|
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lemma assumes "u = Numeral0" shows "2*u = (u::int)" |
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by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
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89 |
(* conclusion matches Rings.ring_1_no_zero_divisors_class.mult_cancel_right2 *) |
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90 |
|
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lemma assumes "i + (j + k) = 3 + (u + y)" |
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92 |
shows "(i + j + 12 + (k::int)) = u + 15 + y" |
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use simproc_setup for cancellation simprocs, to get proper name bindings
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parents:
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93 |
by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
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94 |
|
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95 |
lemma assumes "7 + (j + (i + k)) = y" |
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96 |
shows "(i + j*2 + 12 + (k::int)) = j + 5 + y" |
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parents:
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by (tactic {* test [@{simproc inteq_cancel_numerals}] *}) fact |
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98 |
|
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99 |
lemma assumes "u + (6*z + (4*y + 6*w)) = 6*z' + (4*y' + (6*w' + vv))" |
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100 |
shows "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::int)" |
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parents:
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101 |
by (tactic {* test [@{simproc int_combine_numerals}, @{simproc inteq_cancel_numerals}] *}) fact |
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102 |
|
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103 |
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diff
changeset
|
104 |
subsection {* @{text intless_cancel_numerals} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
105 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
106 |
lemma assumes "y < 2 * b" shows "y - b < (b::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
107 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
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 |
lemma assumes "c + y < 4 * b" shows "y - (3*b + c) < (b::int) - 2*c" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
110 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
111 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
112 |
lemma assumes "i + (j + k) < 8 + (u + y)" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
113 |
shows "(i + j + -3 + (k::int)) < u + 5 + y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
114 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
115 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
116 |
lemma assumes "9 + (i + (j + k)) < u + y" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
117 |
shows "(i + j + 3 + (k::int)) < u + -6 + y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
118 |
by (tactic {* test [@{simproc intless_cancel_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
119 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
120 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
121 |
subsection {* @{text ring_eq_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
122 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
123 |
lemma assumes "3*x = 4*y" shows "9*x = 12 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
124 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
125 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
126 |
lemma assumes "-3*x = 4*y" shows "-99*x = 132 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
127 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
128 |
|
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 int_div_cancel_numeral_factors} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
131 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
132 |
lemma assumes "(3*x) div (4*y) = z" shows "(9*x) div (12*y) = (z::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
133 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
134 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
135 |
lemma assumes "(-3*x) div (4*y) = z" shows "(-99*x) div (132*y) = (z::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
136 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
137 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
138 |
lemma assumes "(111*x) div (-44*y) = z" shows "(999*x) div (-396*y) = (z::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
139 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
140 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
141 |
lemma assumes "(11*x) div (9*y) = z" shows "(-99*x) div (-81*y) = (z::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
142 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
143 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
144 |
lemma assumes "(2*x) div (Numeral1*y) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
145 |
shows "(-2 * x) div (-1 * (y::int)) = z" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
146 |
by (tactic {* test [@{simproc int_div_cancel_numeral_factors}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
147 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
148 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
149 |
subsection {* @{text ring_less_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
150 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
151 |
lemma assumes "3*x < 4*y" shows "9*x < 12 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
152 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
153 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
154 |
lemma assumes "-3*x < 4*y" shows "-99*x < 132 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
155 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
156 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
157 |
lemma assumes "111*x < -44*y" shows "999*x < -396 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
158 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
159 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
160 |
lemma assumes "9*y < 11*x" shows "-99*x < -81 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
161 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
162 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
163 |
lemma assumes "Numeral1*y < 2*x" shows "-2 * x < -(y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
164 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
165 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
166 |
lemma assumes "23*y < Numeral1*x" shows "-x < -23 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
167 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
168 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
169 |
lemma assumes "3*x < 4*y" shows "9*x < 12 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
170 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
171 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
172 |
lemma assumes "-3*x < 4*y" shows "-99*x < 132 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
173 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
174 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
175 |
lemma assumes "111*x < -44*y" shows "999*x < -396 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
176 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
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 |
lemma assumes "9*y < 11*x" shows "-99*x < -81 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
179 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
180 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
181 |
lemma assumes "Numeral1*y < 2*x" shows "-2 * x < -(y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
182 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
183 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
184 |
lemma assumes "23*y < Numeral1*x" shows "-x < -23 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
185 |
by (tactic {* test [@{simproc ring_less_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
186 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
187 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
188 |
subsection {* @{text ring_le_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
189 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
190 |
lemma assumes "3*x \<le> 4*y" shows "9*x \<le> 12 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
191 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
192 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
193 |
lemma assumes "-3*x \<le> 4*y" shows "-99*x \<le> 132 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
194 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
195 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
196 |
lemma assumes "111*x \<le> -44*y" shows "999*x \<le> -396 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
197 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
198 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
199 |
lemma assumes "9*y \<le> 11*x" shows "-99*x \<le> -81 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
200 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
201 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
202 |
lemma assumes "Numeral1*y \<le> 2*x" shows "-2 * x \<le> -1 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
203 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
204 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
205 |
lemma assumes "23*y \<le> Numeral1*x" shows "-x \<le> -23 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
206 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
207 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
208 |
lemma assumes "Numeral1*y \<le> Numeral0" shows "0 \<le> (y::rat) * -2" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
209 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
210 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
211 |
lemma assumes "3*x \<le> 4*y" shows "9*x \<le> 12 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
212 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
213 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
214 |
lemma assumes "-3*x \<le> 4*y" shows "-99*x \<le> 132 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
215 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
216 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
217 |
lemma assumes "111*x \<le> -44*y" shows "999*x \<le> -396 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
218 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
219 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
220 |
lemma assumes "-1*x \<le> Numeral1*y" shows "- ((2::rat) * x) \<le> 2*y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
221 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
222 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
223 |
lemma assumes "9*y \<le> 11*x" shows "-99*x \<le> -81 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
224 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
225 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
226 |
lemma assumes "Numeral1*y \<le> 2*x" shows "-2 * x \<le> -1 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
227 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
228 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
229 |
lemma assumes "23*y \<le> Numeral1*x" shows "-x \<le> -23 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
230 |
by (tactic {* test [@{simproc ring_le_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
231 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
232 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
233 |
subsection {* @{text ring_eq_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
234 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
235 |
lemma assumes "111*x = -44*y" shows "999*x = -396 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
236 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
237 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
238 |
lemma assumes "11*x = 9*y" shows "-99*x = -81 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
239 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
240 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
241 |
lemma assumes "2*x = Numeral1*y" shows "-2 * x = -1 * (y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
242 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
243 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
244 |
lemma assumes "2*x = Numeral1*y" shows "-2 * x = -(y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
245 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
246 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
247 |
lemma assumes "3*x = 4*y" shows "9*x = 12 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
248 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
249 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
250 |
lemma assumes "-3*x = 4*y" shows "-99*x = 132 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
251 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
252 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
253 |
lemma assumes "111*x = -44*y" shows "999*x = -396 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
254 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
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 |
lemma assumes "11*x = 9*y" shows "-99*x = -81 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
257 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
258 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
259 |
lemma assumes "2*x = Numeral1*y" shows "-2 * x = -1 * (y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
260 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
261 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
262 |
lemma assumes "2*x = Numeral1*y" shows "-2 * x = -(y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
263 |
by (tactic {* test [@{simproc ring_eq_cancel_numeral_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
264 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
265 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
266 |
subsection {* @{text field_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
267 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
268 |
lemma assumes "(3*x) / (4*y) = z" shows "(9*x) / (12 * (y::rat)) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
269 |
by (tactic {* test [field_cancel_numeral_factor] *}) fact |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
270 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
271 |
lemma assumes "(-3*x) / (4*y) = z" shows "(-99*x) / (132 * (y::rat)) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
272 |
by (tactic {* test [field_cancel_numeral_factor] *}) fact |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
273 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
274 |
lemma assumes "(111*x) / (-44*y) = z" shows "(999*x) / (-396 * (y::rat)) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
275 |
by (tactic {* test [field_cancel_numeral_factor] *}) fact |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
276 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
277 |
lemma assumes "(11*x) / (9*y) = z" shows "(-99*x) / (-81 * (y::rat)) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
278 |
by (tactic {* test [field_cancel_numeral_factor] *}) fact |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
279 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
280 |
lemma assumes "(2*x) / (Numeral1*y) = z" shows "(-2 * x) / (-1 * (y::rat)) = z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
281 |
by (tactic {* test [field_cancel_numeral_factor] *}) fact |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
282 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
283 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
284 |
subsection {* @{text ring_eq_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
285 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
286 |
lemma assumes "k = 0 \<or> x = y" shows "x*k = k*(y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
287 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
288 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
289 |
lemma assumes "k = 0 \<or> 1 = y" shows "k = k*(y::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
290 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
291 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
292 |
lemma assumes "b = 0 \<or> a*c = 1" shows "a*(b*c) = (b::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
293 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
294 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
295 |
lemma assumes "a = 0 \<or> b = 0 \<or> c = d*x" shows "a*(b*c) = d*(b::int)*(x*a)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
296 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
297 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
298 |
lemma assumes "k = 0 \<or> x = y" shows "x*k = k*(y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
299 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
300 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
301 |
lemma assumes "k = 0 \<or> 1 = y" shows "k = k*(y::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
302 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
303 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
304 |
lemma assumes "b = 0 \<or> a*c = 1" shows "a*(b*c) = (b::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
305 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
306 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
307 |
lemma assumes "a = 0 \<or> b = 0 \<or> c = d*x" shows "a*(b*c) = d*(b::rat)*(x*a)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
308 |
by (tactic {* test [@{simproc ring_eq_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
309 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
310 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
311 |
subsection {* @{text int_div_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
312 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
313 |
lemma assumes "(if k = 0 then 0 else x div y) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
314 |
shows "(x*k) div (k*(y::int)) = (uu::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
315 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
316 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
317 |
lemma assumes "(if k = 0 then 0 else 1 div y) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
318 |
shows "(k) div (k*(y::int)) = (uu::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
319 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
320 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
321 |
lemma assumes "(if b = 0 then 0 else a * c) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
322 |
shows "(a*(b*c)) div ((b::int)) = (uu::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
323 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
324 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
325 |
lemma assumes "(if a = 0 then 0 else if b = 0 then 0 else c div (d * x)) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
326 |
shows "(a*(b*c)) div (d*(b::int)*(x*a)) = (uu::int)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
327 |
by (tactic {* test [@{simproc int_div_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
328 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
329 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
330 |
subsection {* @{text divide_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
331 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
332 |
lemma assumes "(if k = 0 then 0 else x / y) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
333 |
shows "(x*k) / (k*(y::rat)) = (uu::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
334 |
by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
335 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
336 |
lemma assumes "(if k = 0 then 0 else 1 / y) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
337 |
shows "(k) / (k*(y::rat)) = (uu::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
338 |
by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
339 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
340 |
lemma assumes "(if b = 0 then 0 else a * c / 1) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
341 |
shows "(a*(b*c)) / ((b::rat)) = (uu::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
342 |
by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
343 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
344 |
lemma assumes "(if a = 0 then 0 else if b = 0 then 0 else c / (d * x)) = uu" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
345 |
shows "(a*(b*c)) / (d*(b::rat)*(x*a)) = (uu::rat)" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
346 |
by (tactic {* test [@{simproc divide_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
347 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
348 |
lemma shows "a*(b*c)/(y*z) = d*(b::rat)*(x*a)/z" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
349 |
oops -- "FIXME: need simproc to cover this case" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
350 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
351 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
352 |
subsection {* @{text linordered_ring_less_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
353 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
354 |
lemma assumes "0 < z \<Longrightarrow> x < y" shows "(0::rat) < z \<Longrightarrow> x*z < y*z" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
355 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
356 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
357 |
lemma assumes "0 < z \<Longrightarrow> x < y" shows "(0::rat) < z \<Longrightarrow> x*z < z*y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
358 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
359 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
360 |
lemma assumes "0 < z \<Longrightarrow> x < y" shows "(0::rat) < z \<Longrightarrow> z*x < y*z" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
361 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
362 |
|
45270
d5b5c9259afd
fix bug in cancel_factor simprocs so they will work on goals like 'x * y < x * z' where the common term is already on the left
huffman
parents:
45224
diff
changeset
|
363 |
lemma assumes "0 < z \<Longrightarrow> x < y" shows "(0::rat) < z \<Longrightarrow> z*x < z*y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
364 |
by (tactic {* test [@{simproc linordered_ring_less_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
365 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
366 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
367 |
subsection {* @{text linordered_ring_le_cancel_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
368 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
369 |
lemma assumes "0 < z \<Longrightarrow> x \<le> y" shows "(0::rat) < z \<Longrightarrow> x*z \<le> y*z" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
370 |
by (tactic {* test [@{simproc linordered_ring_le_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
371 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
372 |
lemma assumes "0 < z \<Longrightarrow> x \<le> y" shows "(0::rat) < z \<Longrightarrow> z*x \<le> z*y" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
373 |
by (tactic {* test [@{simproc linordered_ring_le_cancel_factor}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
374 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
375 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
376 |
subsection {* @{text field_combine_numerals} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
377 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
378 |
lemma assumes "5 / 6 * x = uu" shows "(x::rat) / 2 + x / 3 = uu" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
379 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
380 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
381 |
lemma assumes "6 / 9 * x + y = uu" shows "(x::rat) / 3 + y + x / 3 = uu" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
382 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
383 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
384 |
lemma assumes "9 / 9 * x = uu" shows "2 * (x::rat) / 3 + x / 3 = uu" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
385 |
by (tactic {* test [@{simproc field_combine_numerals}] *}) fact |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
386 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
387 |
lemma "2/3 * (x::rat) + x / 3 = uu" |
45284
ae78a4ffa81d
use simproc_setup for cancellation simprocs, to get proper name bindings
huffman
parents:
45270
diff
changeset
|
388 |
apply (tactic {* test [@{simproc field_combine_numerals}] *})? |
45224
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
389 |
oops -- "FIXME: test fails" |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
390 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
391 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
392 |
subsection {* @{text field_eq_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
393 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
394 |
text {* TODO: tests for @{text field_eq_cancel_numeral_factor} simproc *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
395 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
396 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
397 |
subsection {* @{text field_cancel_numeral_factor} *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
398 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
399 |
text {* TODO: tests for @{text field_cancel_numeral_factor} simproc *} |
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
400 |
|
b1d5b3820d82
add HOL/ex/Simproc_Tests.thy: testing for Tools/numeral_simprocs.ML
huffman
parents:
diff
changeset
|
401 |
end |