29 "real_of_num" > "HOL4Compat.real_of_num" |
29 "real_of_num" > "HOL4Compat.real_of_num" |
30 "real_lte" > "HOL4Compat.real_lte" |
30 "real_lte" > "HOL4Compat.real_lte" |
31 "real_lt" > "Orderings.linorder_not_le" |
31 "real_lt" > "Orderings.linorder_not_le" |
32 "real_gt" > "HOL4Compat.real_gt" |
32 "real_gt" > "HOL4Compat.real_gt" |
33 "real_ge" > "HOL4Compat.real_ge" |
33 "real_ge" > "HOL4Compat.real_ge" |
34 "real_div" > "Ring_and_Field.field.divide_inverse" |
34 "real_div" > "Ring_and_Field.field_class.divide_inverse" |
35 "pow" > "HOL4Compat.pow" |
35 "pow" > "HOL4Compat.pow" |
36 "abs" > "HOL4Compat.abs" |
36 "abs" > "HOL4Compat.abs" |
37 "SUP_LEMMA3" > "HOL4Real.real.SUP_LEMMA3" |
37 "SUP_LEMMA3" > "HOL4Real.real.SUP_LEMMA3" |
38 "SUP_LEMMA2" > "HOL4Real.real.SUP_LEMMA2" |
38 "SUP_LEMMA2" > "HOL4Real.real.SUP_LEMMA2" |
39 "SUP_LEMMA1" > "HOL4Real.real.SUP_LEMMA1" |
39 "SUP_LEMMA1" > "HOL4Real.real.SUP_LEMMA1" |
145 "REAL_MEAN" > "Ring_and_Field.dense" |
145 "REAL_MEAN" > "Ring_and_Field.dense" |
146 "REAL_LT_TRANS" > "Set.basic_trans_rules_21" |
146 "REAL_LT_TRANS" > "Set.basic_trans_rules_21" |
147 "REAL_LT_TOTAL" > "HOL4Compat.REAL_LT_TOTAL" |
147 "REAL_LT_TOTAL" > "HOL4Compat.REAL_LT_TOTAL" |
148 "REAL_LT_SUB_RADD" > "OrderedGroup.compare_rls_6" |
148 "REAL_LT_SUB_RADD" > "OrderedGroup.compare_rls_6" |
149 "REAL_LT_SUB_LADD" > "OrderedGroup.compare_rls_7" |
149 "REAL_LT_SUB_LADD" > "OrderedGroup.compare_rls_7" |
150 "REAL_LT_RMUL_IMP" > "Ring_and_Field.ordered_semiring_strict.mult_strict_right_mono" |
150 "REAL_LT_RMUL_IMP" > "Ring_and_Field.ordered_semiring_strict_class.mult_strict_right_mono" |
151 "REAL_LT_RMUL_0" > "HOL4Real.real.REAL_LT_RMUL_0" |
151 "REAL_LT_RMUL_0" > "HOL4Real.real.REAL_LT_RMUL_0" |
152 "REAL_LT_RMUL" > "RealDef.real_mult_less_iff1" |
152 "REAL_LT_RMUL" > "RealDef.real_mult_less_iff1" |
153 "REAL_LT_REFL" > "Orderings.order_less_irrefl" |
153 "REAL_LT_REFL" > "Orderings.order_less_irrefl" |
154 "REAL_LT_RDIV_EQ" > "Ring_and_Field.pos_less_divide_eq" |
154 "REAL_LT_RDIV_EQ" > "Ring_and_Field.pos_less_divide_eq" |
155 "REAL_LT_RDIV_0" > "HOL4Real.real.REAL_LT_RDIV_0" |
155 "REAL_LT_RDIV_0" > "HOL4Real.real.REAL_LT_RDIV_0" |
159 "REAL_LT_NEGTOTAL" > "HOL4Real.real.REAL_LT_NEGTOTAL" |
159 "REAL_LT_NEGTOTAL" > "HOL4Real.real.REAL_LT_NEGTOTAL" |
160 "REAL_LT_NEG" > "OrderedGroup.neg_less_iff_less" |
160 "REAL_LT_NEG" > "OrderedGroup.neg_less_iff_less" |
161 "REAL_LT_MULTIPLE" > "HOL4Real.real.REAL_LT_MULTIPLE" |
161 "REAL_LT_MULTIPLE" > "HOL4Real.real.REAL_LT_MULTIPLE" |
162 "REAL_LT_MUL2" > "Ring_and_Field.mult_strict_mono'" |
162 "REAL_LT_MUL2" > "Ring_and_Field.mult_strict_mono'" |
163 "REAL_LT_MUL" > "Ring_and_Field.mult_pos_pos" |
163 "REAL_LT_MUL" > "Ring_and_Field.mult_pos_pos" |
164 "REAL_LT_LMUL_IMP" > "Ring_and_Field.ordered_comm_semiring_strict.mult_strict_mono" |
164 "REAL_LT_LMUL_IMP" > "Ring_and_Field.ordered_comm_semiring_strict_class.mult_strict_mono" |
165 "REAL_LT_LMUL_0" > "HOL4Real.real.REAL_LT_LMUL_0" |
165 "REAL_LT_LMUL_0" > "HOL4Real.real.REAL_LT_LMUL_0" |
166 "REAL_LT_LMUL" > "HOL4Real.real.REAL_LT_LMUL" |
166 "REAL_LT_LMUL" > "HOL4Real.real.REAL_LT_LMUL" |
167 "REAL_LT_LE" > "Orderings.order.order_less_le" |
167 "REAL_LT_LE" > "Orderings.order_class.order_less_le" |
168 "REAL_LT_LDIV_EQ" > "Ring_and_Field.pos_divide_less_eq" |
168 "REAL_LT_LDIV_EQ" > "Ring_and_Field.pos_divide_less_eq" |
169 "REAL_LT_LADD" > "OrderedGroup.add_less_cancel_left" |
169 "REAL_LT_LADD" > "OrderedGroup.add_less_cancel_left" |
170 "REAL_LT_INV_EQ" > "Ring_and_Field.inverse_positive_iff_positive" |
170 "REAL_LT_INV_EQ" > "Ring_and_Field.inverse_positive_iff_positive" |
171 "REAL_LT_INV" > "Ring_and_Field.less_imp_inverse_less" |
171 "REAL_LT_INV" > "Ring_and_Field.less_imp_inverse_less" |
172 "REAL_LT_IMP_NE" > "Orderings.less_imp_neq" |
172 "REAL_LT_IMP_NE" > "Orderings.less_imp_neq" |
186 "REAL_LT_ADDL" > "HOL4Real.real.REAL_LT_ADDL" |
186 "REAL_LT_ADDL" > "HOL4Real.real.REAL_LT_ADDL" |
187 "REAL_LT_ADD2" > "OrderedGroup.add_strict_mono" |
187 "REAL_LT_ADD2" > "OrderedGroup.add_strict_mono" |
188 "REAL_LT_ADD1" > "HOL4Real.real.REAL_LT_ADD1" |
188 "REAL_LT_ADD1" > "HOL4Real.real.REAL_LT_ADD1" |
189 "REAL_LT_ADD" > "OrderedGroup.add_pos_pos" |
189 "REAL_LT_ADD" > "OrderedGroup.add_pos_pos" |
190 "REAL_LT_1" > "HOL4Real.real.REAL_LT_1" |
190 "REAL_LT_1" > "HOL4Real.real.REAL_LT_1" |
191 "REAL_LT_01" > "Ring_and_Field.ordered_semidom.zero_less_one" |
191 "REAL_LT_01" > "Ring_and_Field.ordered_semidom_class.zero_less_one" |
192 "REAL_LTE_TRANS" > "Set.basic_trans_rules_24" |
192 "REAL_LTE_TRANS" > "Set.basic_trans_rules_24" |
193 "REAL_LTE_TOTAL" > "HOL4Real.real.REAL_LTE_TOTAL" |
193 "REAL_LTE_TOTAL" > "HOL4Real.real.REAL_LTE_TOTAL" |
194 "REAL_LTE_ANTSYM" > "HOL4Real.real.REAL_LTE_ANTSYM" |
194 "REAL_LTE_ANTSYM" > "HOL4Real.real.REAL_LTE_ANTSYM" |
195 "REAL_LTE_ADD2" > "OrderedGroup.add_less_le_mono" |
195 "REAL_LTE_ADD2" > "OrderedGroup.add_less_le_mono" |
196 "REAL_LTE_ADD" > "OrderedGroup.add_pos_nonneg" |
196 "REAL_LTE_ADD" > "OrderedGroup.add_pos_nonneg" |
197 "REAL_LT1_POW2" > "HOL4Real.real.REAL_LT1_POW2" |
197 "REAL_LT1_POW2" > "HOL4Real.real.REAL_LT1_POW2" |
198 "REAL_LT" > "RealDef.real_of_nat_less_iff" |
198 "REAL_LT" > "RealDef.real_of_nat_less_iff" |
199 "REAL_LNEG_UNIQ" > "HOL4Real.real.REAL_LNEG_UNIQ" |
199 "REAL_LNEG_UNIQ" > "HOL4Real.real.REAL_LNEG_UNIQ" |
200 "REAL_LINV_UNIQ" > "HOL4Real.real.REAL_LINV_UNIQ" |
200 "REAL_LINV_UNIQ" > "HOL4Real.real.REAL_LINV_UNIQ" |
201 "REAL_LE_TRANS" > "Set.basic_trans_rules_25" |
201 "REAL_LE_TRANS" > "Set.basic_trans_rules_25" |
202 "REAL_LE_TOTAL" > "Orderings.linorder.linorder_linear" |
202 "REAL_LE_TOTAL" > "Orderings.linorder_class.linorder_linear" |
203 "REAL_LE_SUB_RADD" > "OrderedGroup.compare_rls_8" |
203 "REAL_LE_SUB_RADD" > "OrderedGroup.compare_rls_8" |
204 "REAL_LE_SUB_LADD" > "OrderedGroup.compare_rls_9" |
204 "REAL_LE_SUB_LADD" > "OrderedGroup.compare_rls_9" |
205 "REAL_LE_SQUARE" > "Ring_and_Field.zero_le_square" |
205 "REAL_LE_SQUARE" > "Ring_and_Field.zero_le_square" |
206 "REAL_LE_RNEG" > "OrderedGroup.le_eq_neg" |
206 "REAL_LE_RNEG" > "OrderedGroup.le_eq_neg" |
207 "REAL_LE_RMUL_IMP" > "Ring_and_Field.pordered_semiring.mult_right_mono" |
207 "REAL_LE_RMUL_IMP" > "Ring_and_Field.pordered_semiring_class.mult_right_mono" |
208 "REAL_LE_RMUL" > "RealDef.real_mult_le_cancel_iff1" |
208 "REAL_LE_RMUL" > "RealDef.real_mult_le_cancel_iff1" |
209 "REAL_LE_REFL" > "Finite_Set.max.f_below.below_refl" |
209 "REAL_LE_REFL" > "Finite_Set.max.f_below.below_refl" |
210 "REAL_LE_RDIV_EQ" > "Ring_and_Field.pos_le_divide_eq" |
210 "REAL_LE_RDIV_EQ" > "Ring_and_Field.pos_le_divide_eq" |
211 "REAL_LE_RDIV" > "Ring_and_Field.mult_imp_le_div_pos" |
211 "REAL_LE_RDIV" > "Ring_and_Field.mult_imp_le_div_pos" |
212 "REAL_LE_RADD" > "OrderedGroup.add_le_cancel_right" |
212 "REAL_LE_RADD" > "OrderedGroup.add_le_cancel_right" |
218 "REAL_LE_NEG" > "OrderedGroup.neg_le_iff_le" |
218 "REAL_LE_NEG" > "OrderedGroup.neg_le_iff_le" |
219 "REAL_LE_MUL2" > "HOL4Real.real.REAL_LE_MUL2" |
219 "REAL_LE_MUL2" > "HOL4Real.real.REAL_LE_MUL2" |
220 "REAL_LE_MUL" > "Ring_and_Field.mult_nonneg_nonneg" |
220 "REAL_LE_MUL" > "Ring_and_Field.mult_nonneg_nonneg" |
221 "REAL_LE_LT" > "Orderings.order_le_less" |
221 "REAL_LE_LT" > "Orderings.order_le_less" |
222 "REAL_LE_LNEG" > "RealDef.real_0_le_add_iff" |
222 "REAL_LE_LNEG" > "RealDef.real_0_le_add_iff" |
223 "REAL_LE_LMUL_IMP" > "Ring_and_Field.pordered_comm_semiring.mult_mono" |
223 "REAL_LE_LMUL_IMP" > "Ring_and_Field.pordered_comm_semiring_class.mult_mono" |
224 "REAL_LE_LMUL" > "RealDef.real_mult_le_cancel_iff2" |
224 "REAL_LE_LMUL" > "RealDef.real_mult_le_cancel_iff2" |
225 "REAL_LE_LDIV_EQ" > "Ring_and_Field.pos_divide_le_eq" |
225 "REAL_LE_LDIV_EQ" > "Ring_and_Field.pos_divide_le_eq" |
226 "REAL_LE_LDIV" > "Ring_and_Field.mult_imp_div_pos_le" |
226 "REAL_LE_LDIV" > "Ring_and_Field.mult_imp_div_pos_le" |
227 "REAL_LE_LADD_IMP" > "OrderedGroup.pordered_ab_semigroup_add.add_left_mono" |
227 "REAL_LE_LADD_IMP" > "OrderedGroup.pordered_ab_semigroup_add_class.add_left_mono" |
228 "REAL_LE_LADD" > "OrderedGroup.add_le_cancel_left" |
228 "REAL_LE_LADD" > "OrderedGroup.add_le_cancel_left" |
229 "REAL_LE_INV_EQ" > "Ring_and_Field.inverse_nonnegative_iff_nonnegative" |
229 "REAL_LE_INV_EQ" > "Ring_and_Field.inverse_nonnegative_iff_nonnegative" |
230 "REAL_LE_INV" > "HOL4Real.real.REAL_LE_INV" |
230 "REAL_LE_INV" > "HOL4Real.real.REAL_LE_INV" |
231 "REAL_LE_DOUBLE" > "OrderedGroup.zero_le_double_add_iff_zero_le_single_add" |
231 "REAL_LE_DOUBLE" > "OrderedGroup.zero_le_double_add_iff_zero_le_single_add" |
232 "REAL_LE_DIV" > "HOL4Real.real.REAL_LE_DIV" |
232 "REAL_LE_DIV" > "HOL4Real.real.REAL_LE_DIV" |
249 "REAL_INV_MUL" > "HOL4Real.real.REAL_INV_MUL" |
249 "REAL_INV_MUL" > "HOL4Real.real.REAL_INV_MUL" |
250 "REAL_INV_LT1" > "RealDef.real_inverse_gt_one" |
250 "REAL_INV_LT1" > "RealDef.real_inverse_gt_one" |
251 "REAL_INV_INV" > "Ring_and_Field.inverse_inverse_eq" |
251 "REAL_INV_INV" > "Ring_and_Field.inverse_inverse_eq" |
252 "REAL_INV_EQ_0" > "Ring_and_Field.inverse_nonzero_iff_nonzero" |
252 "REAL_INV_EQ_0" > "Ring_and_Field.inverse_nonzero_iff_nonzero" |
253 "REAL_INV_1OVER" > "Ring_and_Field.inverse_eq_divide" |
253 "REAL_INV_1OVER" > "Ring_and_Field.inverse_eq_divide" |
254 "REAL_INV_0" > "Ring_and_Field.division_by_zero.inverse_zero" |
254 "REAL_INV_0" > "Ring_and_Field.division_by_zero_class.inverse_zero" |
255 "REAL_INVINV" > "Ring_and_Field.nonzero_inverse_inverse_eq" |
255 "REAL_INVINV" > "Ring_and_Field.nonzero_inverse_inverse_eq" |
256 "REAL_INV1" > "Ring_and_Field.inverse_1" |
256 "REAL_INV1" > "Ring_and_Field.inverse_1" |
257 "REAL_INJ" > "RealDef.real_of_nat_inject" |
257 "REAL_INJ" > "RealDef.real_of_nat_inject" |
258 "REAL_HALF_DOUBLE" > "RComplete.real_sum_of_halves" |
258 "REAL_HALF_DOUBLE" > "RComplete.real_sum_of_halves" |
259 "REAL_FACT_NZ" > "HOL4Real.real.REAL_FACT_NZ" |
259 "REAL_FACT_NZ" > "HOL4Real.real.REAL_FACT_NZ" |