updated;

--- a/src/HOL/Import/HOL/HOL4Real.thy	Fri May 21 21:28:58 2004 +0200
+++ b/src/HOL/Import/HOL/HOL4Real.thy	Fri May 21 21:42:05 2004 +0200
@@ -272,10 +272,6 @@
 lemma REAL_LE_NEGTOTAL: "ALL x::real. (0::real) <= x | (0::real) <= - x"
   by (import real REAL_LE_NEGTOTAL)
 
-lemma REAL_LE_MUL: "ALL (x::real) y::real.
-   (0::real) <= x & (0::real) <= y --> (0::real) <= x * y"
-  by (import real REAL_LE_MUL)
-
 lemma REAL_LT_ADDNEG: "ALL (x::real) (y::real) z::real. (y < x + - z) = (y + z < x)"
   by (import real REAL_LT_ADDNEG)
 
@@ -285,8 +281,11 @@
 lemma REAL_LT_ADD1: "ALL (x::real) y::real. x <= y --> x < y + (1::real)"
   by (import real REAL_LT_ADD1)
 
-lemma REAL_LE_DOUBLE: "ALL x::real. ((0::real) <= x + x) = ((0::real) <= x)"
-  by (import real REAL_LE_DOUBLE)
+lemma REAL_SUB_ADD2: "ALL (x::real) y::real. y + (x - y) = x"
+  by (import real REAL_SUB_ADD2)
+
+lemma REAL_ADD_SUB: "ALL (x::real) y::real. x + y - x = y"
+  by (import real REAL_ADD_SUB)
 
 lemma REAL_NEG_EQ: "ALL (x::real) y::real. (- x = y) = (x = - y)"
   by (import real REAL_NEG_EQ)
@@ -691,9 +690,6 @@
 lemma SUM_CANCEL: "ALL f n d. real.sum (n, d) (%n. f (Suc n) - f n) = f (n + d) - f n"
   by (import real SUM_CANCEL)
 
-lemma REAL_LE_RNEG: "ALL (x::real) y::real. (x <= - y) = (x + y <= (0::real))"
-  by (import real REAL_LE_RNEG)
-
 lemma REAL_EQ_RDIV_EQ: "ALL (x::real) (xa::real) xb::real.
    (0::real) < xb --> (x = xa / xb) = (x * xb = xa)"
   by (import real REAL_EQ_RDIV_EQ)

--- a/src/HOL/Import/HOL/arithmetic.imp	Fri May 21 21:28:58 2004 +0200
+++ b/src/HOL/Import/HOL/arithmetic.imp	Fri May 21 21:42:05 2004 +0200
@@ -166,8 +166,8 @@
   "LESS_MONO_REV" > "Nat.Suc_less_SucD"
   "LESS_MONO_MULT" > "Nat.mult_le_mono1"
   "LESS_MONO_EQ" > "Nat.Suc_less_eq"
-  "LESS_MONO_ADD_INV" > "Ring_and_Field.add_less_imp_less_right"
-  "LESS_MONO_ADD_EQ" > "Ring_and_Field.add_less_cancel_right"
+  "LESS_MONO_ADD_INV" > "OrderedGroup.add_less_imp_less_right"
+  "LESS_MONO_ADD_EQ" > "OrderedGroup.add_less_cancel_right"
   "LESS_MONO_ADD" > "Nat.add_less_mono1"
   "LESS_MOD" > "Divides.mod_less"
   "LESS_LESS_SUC" > "HOL4Base.arithmetic.LESS_LESS_SUC"
@@ -180,7 +180,7 @@
   "LESS_EQ_SUC_REFL" > "HOL4Base.arithmetic.LESS_EQ_SUC_REFL"
   "LESS_EQ_SUB_LESS" > "HOL4Base.arithmetic.LESS_EQ_SUB_LESS"
   "LESS_EQ_REFL" > "Nat.le_refl"
-  "LESS_EQ_MONO_ADD_EQ" > "Ring_and_Field.add_le_cancel_right"
+  "LESS_EQ_MONO_ADD_EQ" > "OrderedGroup.add_le_cancel_right"
   "LESS_EQ_MONO" > "Nat.Suc_le_mono"
   "LESS_EQ_LESS_TRANS" > "Nat.le_less_trans"
   "LESS_EQ_LESS_EQ_MONO" > "Nat.add_le_mono"

--- a/src/HOL/Import/HOL/real.imp	Fri May 21 21:28:58 2004 +0200
+++ b/src/HOL/Import/HOL/real.imp	Fri May 21 21:42:05 2004 +0200
@@ -25,7 +25,7 @@
   "sumc" > "HOL4Real.real.sumc"
   "sum_def" > "HOL4Real.real.sum_def"
   "sum" > "HOL4Real.real.sum"
-  "real_sub" > "Ring_and_Field.compare_rls_1"
+  "real_sub" > "OrderedGroup.compare_rls_1"
   "real_of_num" > "HOL4Compat.real_of_num"
   "real_lte" > "HOL4Compat.real_lte"
   "real_lt" > "HOL.linorder_not_le"
@@ -74,21 +74,21 @@
   "REAL_SUB_TRIANGLE" > "HOL4Real.real.REAL_SUB_TRIANGLE"
   "REAL_SUB_SUB2" > "HOL4Real.real.REAL_SUB_SUB2"
   "REAL_SUB_SUB" > "HOL4Real.real.REAL_SUB_SUB"
-  "REAL_SUB_RZERO" > "Ring_and_Field.diff_0_right"
-  "REAL_SUB_RNEG" > "Ring_and_Field.diff_minus_eq_add"
-  "REAL_SUB_REFL" > "Ring_and_Field.diff_self"
+  "REAL_SUB_RZERO" > "OrderedGroup.diff_0_right"
+  "REAL_SUB_RNEG" > "OrderedGroup.diff_minus_eq_add"
+  "REAL_SUB_REFL" > "OrderedGroup.diff_self"
   "REAL_SUB_RDISTRIB" > "Ring_and_Field.ring_eq_simps_6"
   "REAL_SUB_NEG2" > "HOL4Real.real.REAL_SUB_NEG2"
-  "REAL_SUB_LZERO" > "Ring_and_Field.diff_0"
+  "REAL_SUB_LZERO" > "OrderedGroup.diff_0"
   "REAL_SUB_LT" > "RealDef.real_0_less_diff_iff"
   "REAL_SUB_LNEG" > "HOL4Real.real.REAL_SUB_LNEG"
   "REAL_SUB_LE" > "RealDef.real_0_le_diff_iff"
   "REAL_SUB_LDISTRIB" > "Ring_and_Field.ring_eq_simps_7"
   "REAL_SUB_INV2" > "HOL4Real.real.REAL_SUB_INV2"
-  "REAL_SUB_ADD2" > "Ring_and_Field.add_minus_self_left"
-  "REAL_SUB_ADD" > "Ring_and_Field.minus_add_self"
+  "REAL_SUB_ADD2" > "HOL4Real.real.REAL_SUB_ADD2"
+  "REAL_SUB_ADD" > "OrderedGroup.diff_add_cancel"
   "REAL_SUB_ABS" > "HOL4Real.real.REAL_SUB_ABS"
-  "REAL_SUB_0" > "Ring_and_Field.eq_iff_diff_eq_0"
+  "REAL_SUB_0" > "OrderedGroup.eq_iff_diff_eq_0"
   "REAL_RNEG_UNIQ" > "RealDef.real_add_eq_0_iff"
   "REAL_RINV_UNIQ" > "RealDef.real_inverse_unique"
   "REAL_RDISTRIB" > "Ring_and_Field.ring_eq_simps_4"
@@ -113,31 +113,31 @@
   "REAL_NZ_IMP_LT" > "HOL4Real.real.REAL_NZ_IMP_LT"
   "REAL_NOT_LT" > "HOL4Compat.real_lte"
   "REAL_NOT_LE" > "HOL.linorder_not_le"
-  "REAL_NEG_SUB" > "Ring_and_Field.minus_diff_eq"
+  "REAL_NEG_SUB" > "OrderedGroup.minus_diff_eq"
   "REAL_NEG_RMUL" > "Ring_and_Field.minus_mult_right"
-  "REAL_NEG_NEG" > "Ring_and_Field.minus_minus"
+  "REAL_NEG_NEG" > "OrderedGroup.minus_minus"
   "REAL_NEG_MUL2" > "Ring_and_Field.minus_mult_minus"
   "REAL_NEG_MINUS1" > "HOL4Real.real.REAL_NEG_MINUS1"
-  "REAL_NEG_LT0" > "Ring_and_Field.neg_less_0_iff_less"
+  "REAL_NEG_LT0" > "OrderedGroup.neg_less_0_iff_less"
   "REAL_NEG_LMUL" > "Ring_and_Field.minus_mult_left"
-  "REAL_NEG_LE0" > "Ring_and_Field.neg_le_0_iff_le"
+  "REAL_NEG_LE0" > "OrderedGroup.neg_le_0_iff_le"
   "REAL_NEG_INV" > "Ring_and_Field.nonzero_inverse_minus_eq"
-  "REAL_NEG_GT0" > "Ring_and_Field.neg_0_less_iff_less"
-  "REAL_NEG_GE0" > "Ring_and_Field.neg_0_le_iff_le"
-  "REAL_NEG_EQ0" > "Ring_and_Field.neg_equal_0_iff_equal"
+  "REAL_NEG_GT0" > "OrderedGroup.neg_0_less_iff_less"
+  "REAL_NEG_GE0" > "OrderedGroup.neg_0_le_iff_le"
+  "REAL_NEG_EQ0" > "OrderedGroup.neg_equal_0_iff_equal"
   "REAL_NEG_EQ" > "HOL4Real.real.REAL_NEG_EQ"
-  "REAL_NEG_ADD" > "Ring_and_Field.minus_add_distrib"
-  "REAL_NEG_0" > "Ring_and_Field.minus_zero"
-  "REAL_NEGNEG" > "Ring_and_Field.minus_minus"
+  "REAL_NEG_ADD" > "OrderedGroup.minus_add_distrib"
+  "REAL_NEG_0" > "OrderedGroup.minus_zero"
+  "REAL_NEGNEG" > "OrderedGroup.minus_minus"
   "REAL_MUL_SYM" > "Ring_and_Field.ring_eq_simps_2"
   "REAL_MUL_RZERO" > "Ring_and_Field.mult_zero_right"
   "REAL_MUL_RNEG" > "Ring_and_Field.minus_mult_right"
   "REAL_MUL_RINV" > "Ring_and_Field.right_inverse"
-  "REAL_MUL_RID" > "Ring_and_Field.mult_1_right"
+  "REAL_MUL_RID" > "OrderedGroup.monoid_mult.mult_1_right"
   "REAL_MUL_LZERO" > "Ring_and_Field.mult_zero_left"
   "REAL_MUL_LNEG" > "Ring_and_Field.minus_mult_left"
   "REAL_MUL_LINV" > "HOL4Compat.REAL_MUL_LINV"
-  "REAL_MUL_LID" > "Ring_and_Field.almost_semiring.mult_1"
+  "REAL_MUL_LID" > "OrderedGroup.comm_monoid_mult.mult_1"
   "REAL_MUL_ASSOC" > "HOL4Compat.REAL_MUL_ASSOC"
   "REAL_MUL" > "RealDef.real_of_nat_mult"
   "REAL_MIDDLE2" > "HOL4Real.real.REAL_MIDDLE2"
@@ -145,33 +145,33 @@
   "REAL_MEAN" > "Ring_and_Field.dense"
   "REAL_LT_TRANS" > "Set.basic_trans_rules_21"
   "REAL_LT_TOTAL" > "HOL4Compat.REAL_LT_TOTAL"
-  "REAL_LT_SUB_RADD" > "Ring_and_Field.compare_rls_6"
-  "REAL_LT_SUB_LADD" > "Ring_and_Field.compare_rls_7"
-  "REAL_LT_RMUL_IMP" > "Ring_and_Field.mult_strict_right_mono"
+  "REAL_LT_SUB_RADD" > "OrderedGroup.compare_rls_6"
+  "REAL_LT_SUB_LADD" > "OrderedGroup.compare_rls_7"
+  "REAL_LT_RMUL_IMP" > "Ring_and_Field.ordered_semiring_strict.mult_strict_right_mono"
   "REAL_LT_RMUL_0" > "HOL4Real.real.REAL_LT_RMUL_0"
   "REAL_LT_RMUL" > "RealDef.real_mult_less_iff1"
   "REAL_LT_REFL" > "HOL.order_less_irrefl"
   "REAL_LT_RDIV_EQ" > "Ring_and_Field.pos_less_divide_eq"
   "REAL_LT_RDIV_0" > "HOL4Real.real.REAL_LT_RDIV_0"
   "REAL_LT_RDIV" > "HOL4Real.real.REAL_LT_RDIV"
-  "REAL_LT_RADD" > "Ring_and_Field.add_less_cancel_right"
+  "REAL_LT_RADD" > "OrderedGroup.add_less_cancel_right"
   "REAL_LT_NZ" > "HOL4Real.real.REAL_LT_NZ"
   "REAL_LT_NEGTOTAL" > "HOL4Real.real.REAL_LT_NEGTOTAL"
-  "REAL_LT_NEG" > "Ring_and_Field.neg_less_iff_less"
+  "REAL_LT_NEG" > "OrderedGroup.neg_less_iff_less"
   "REAL_LT_MULTIPLE" > "HOL4Real.real.REAL_LT_MULTIPLE"
   "REAL_LT_MUL2" > "Ring_and_Field.mult_strict_mono'"
   "REAL_LT_MUL" > "Ring_and_Field.mult_pos"
-  "REAL_LT_LMUL_IMP" > "Ring_and_Field.almost_ordered_semiring.mult_strict_left_mono"
+  "REAL_LT_LMUL_IMP" > "Ring_and_Field.ordered_comm_semiring_strict.mult_strict_mono"
   "REAL_LT_LMUL_0" > "HOL4Real.real.REAL_LT_LMUL_0"
   "REAL_LT_LMUL" > "HOL4Real.real.REAL_LT_LMUL"
   "REAL_LT_LE" > "HOL.order.order_less_le"
   "REAL_LT_LDIV_EQ" > "Ring_and_Field.pos_divide_less_eq"
-  "REAL_LT_LADD" > "Ring_and_Field.add_less_cancel_left"
+  "REAL_LT_LADD" > "OrderedGroup.add_less_cancel_left"
   "REAL_LT_INV_EQ" > "Ring_and_Field.inverse_positive_iff_positive"
   "REAL_LT_INV" > "Ring_and_Field.less_imp_inverse_less"
   "REAL_LT_IMP_NE" > "HOL.less_imp_neq"
   "REAL_LT_IMP_LE" > "HOL.order_less_imp_le"
-  "REAL_LT_IADD" > "Ring_and_Field.add_strict_left_mono"
+  "REAL_LT_IADD" > "OrderedGroup.add_strict_left_mono"
   "REAL_LT_HALF2" > "HOL4Real.real.REAL_LT_HALF2"
   "REAL_LT_HALF1" > "NatSimprocs.half_gt_zero_iff"
   "REAL_LT_GT" > "HOL.order_less_not_sym"
@@ -179,20 +179,20 @@
   "REAL_LT_FRACTION" > "HOL4Real.real.REAL_LT_FRACTION"
   "REAL_LT_DIV" > "HOL4Real.real.REAL_LT_DIV"
   "REAL_LT_ANTISYM" > "HOL4Real.real.REAL_LT_ANTISYM"
-  "REAL_LT_ADD_SUB" > "Ring_and_Field.compare_rls_7"
+  "REAL_LT_ADD_SUB" > "OrderedGroup.compare_rls_7"
   "REAL_LT_ADDR" > "HOL4Real.real.REAL_LT_ADDR"
   "REAL_LT_ADDNEG2" > "HOL4Real.real.REAL_LT_ADDNEG2"
   "REAL_LT_ADDNEG" > "HOL4Real.real.REAL_LT_ADDNEG"
   "REAL_LT_ADDL" > "HOL4Real.real.REAL_LT_ADDL"
-  "REAL_LT_ADD2" > "Ring_and_Field.add_strict_mono"
+  "REAL_LT_ADD2" > "OrderedGroup.add_strict_mono"
   "REAL_LT_ADD1" > "HOL4Real.real.REAL_LT_ADD1"
   "REAL_LT_ADD" > "RealDef.real_add_order"
   "REAL_LT_1" > "HOL4Real.real.REAL_LT_1"
-  "REAL_LT_01" > "Ring_and_Field.ordered_semiring.zero_less_one"
+  "REAL_LT_01" > "Ring_and_Field.ordered_semidom.zero_less_one"
   "REAL_LTE_TRANS" > "Set.basic_trans_rules_24"
   "REAL_LTE_TOTAL" > "HOL4Real.real.REAL_LTE_TOTAL"
   "REAL_LTE_ANTSYM" > "HOL4Real.real.REAL_LTE_ANTSYM"
-  "REAL_LTE_ADD2" > "Ring_and_Field.add_less_le_mono"
+  "REAL_LTE_ADD2" > "OrderedGroup.add_less_le_mono"
   "REAL_LTE_ADD" > "HOL4Real.real.REAL_LTE_ADD"
   "REAL_LT1_POW2" > "HOL4Real.real.REAL_LT1_POW2"
   "REAL_LT" > "RealDef.real_of_nat_less_iff"
@@ -200,46 +200,46 @@
   "REAL_LINV_UNIQ" > "HOL4Real.real.REAL_LINV_UNIQ"
   "REAL_LE_TRANS" > "Set.basic_trans_rules_25"
   "REAL_LE_TOTAL" > "HOL.linorder.linorder_linear"
-  "REAL_LE_SUB_RADD" > "Ring_and_Field.compare_rls_8"
-  "REAL_LE_SUB_LADD" > "Ring_and_Field.compare_rls_9"
+  "REAL_LE_SUB_RADD" > "OrderedGroup.compare_rls_8"
+  "REAL_LE_SUB_LADD" > "OrderedGroup.compare_rls_9"
   "REAL_LE_SQUARE" > "Ring_and_Field.zero_le_square"
-  "REAL_LE_RNEG" > "HOL4Real.real.REAL_LE_RNEG"
-  "REAL_LE_RMUL_IMP" > "Ring_and_Field.mult_right_mono"
+  "REAL_LE_RNEG" > "OrderedGroup.le_eq_neg"
+  "REAL_LE_RMUL_IMP" > "Ring_and_Field.pordered_semiring.mult_right_mono"
   "REAL_LE_RMUL" > "RealDef.real_mult_le_cancel_iff1"
   "REAL_LE_REFL" > "HOL.order.order_refl"
   "REAL_LE_RDIV_EQ" > "Ring_and_Field.pos_le_divide_eq"
   "REAL_LE_RDIV" > "HOL4Real.real.REAL_LE_RDIV"
-  "REAL_LE_RADD" > "Ring_and_Field.add_le_cancel_right"
+  "REAL_LE_RADD" > "OrderedGroup.add_le_cancel_right"
   "REAL_LE_POW2" > "NatBin.zero_le_power2"
   "REAL_LE_NEGTOTAL" > "HOL4Real.real.REAL_LE_NEGTOTAL"
-  "REAL_LE_NEGR" > "Ring_and_Field.le_minus_self_iff"
-  "REAL_LE_NEGL" > "Ring_and_Field.minus_le_self_iff"
-  "REAL_LE_NEG2" > "Ring_and_Field.neg_le_iff_le"
-  "REAL_LE_NEG" > "Ring_and_Field.neg_le_iff_le"
+  "REAL_LE_NEGR" > "OrderedGroup.le_minus_self_iff"
+  "REAL_LE_NEGL" > "OrderedGroup.minus_le_self_iff"
+  "REAL_LE_NEG2" > "OrderedGroup.neg_le_iff_le"
+  "REAL_LE_NEG" > "OrderedGroup.neg_le_iff_le"
   "REAL_LE_MUL2" > "HOL4Real.real.REAL_LE_MUL2"
-  "REAL_LE_MUL" > "HOL4Real.real.REAL_LE_MUL"
+  "REAL_LE_MUL" > "Ring_and_Field.mult_pos_le"
   "REAL_LE_LT" > "HOL.order_le_less"
   "REAL_LE_LNEG" > "RealDef.real_0_le_add_iff"
-  "REAL_LE_LMUL_IMP" > "Ring_and_Field.mult_left_mono"
+  "REAL_LE_LMUL_IMP" > "Ring_and_Field.pordered_comm_semiring.mult_mono"
   "REAL_LE_LMUL" > "RealDef.real_mult_le_cancel_iff2"
   "REAL_LE_LDIV_EQ" > "Ring_and_Field.pos_divide_le_eq"
   "REAL_LE_LDIV" > "HOL4Real.real.REAL_LE_LDIV"
-  "REAL_LE_LADD_IMP" > "Ring_and_Field.almost_ordered_semiring.add_left_mono"
-  "REAL_LE_LADD" > "Ring_and_Field.add_le_cancel_left"
+  "REAL_LE_LADD_IMP" > "OrderedGroup.pordered_ab_semigroup_add.add_left_mono"
+  "REAL_LE_LADD" > "OrderedGroup.add_le_cancel_left"
   "REAL_LE_INV_EQ" > "Ring_and_Field.inverse_nonnegative_iff_nonnegative"
   "REAL_LE_INV" > "HOL4Real.real.REAL_LE_INV"
-  "REAL_LE_DOUBLE" > "HOL4Real.real.REAL_LE_DOUBLE"
+  "REAL_LE_DOUBLE" > "OrderedGroup.zero_le_double_add_iff_zero_le_single_add"
   "REAL_LE_DIV" > "HOL4Real.real.REAL_LE_DIV"
   "REAL_LE_ANTISYM" > "HOL.order_eq_iff"
   "REAL_LE_ADDR" > "HOL4Real.real.REAL_LE_ADDR"
   "REAL_LE_ADDL" > "HOL4Real.real.REAL_LE_ADDL"
-  "REAL_LE_ADD2" > "Ring_and_Field.add_mono"
+  "REAL_LE_ADD2" > "OrderedGroup.add_mono"
   "REAL_LE_ADD" > "RealDef.real_le_add_order"
   "REAL_LE_01" > "Ring_and_Field.zero_le_one"
   "REAL_LET_TRANS" > "Set.basic_trans_rules_23"
   "REAL_LET_TOTAL" > "HOL4Real.real.REAL_LET_TOTAL"
   "REAL_LET_ANTISYM" > "HOL4Real.real.REAL_LET_ANTISYM"
-  "REAL_LET_ADD2" > "Ring_and_Field.add_le_less_mono"
+  "REAL_LET_ADD2" > "OrderedGroup.add_le_less_mono"
   "REAL_LET_ADD" > "HOL4Real.real.REAL_LET_ADD"
   "REAL_LE1_POW2" > "HOL4Real.real.REAL_LE1_POW2"
   "REAL_LE" > "RealDef.real_of_nat_le_iff"
@@ -262,14 +262,14 @@
   "REAL_EQ_RMUL_IMP" > "Ring_and_Field.field_mult_cancel_right_lemma"
   "REAL_EQ_RMUL" > "Ring_and_Field.field_mult_cancel_right"
   "REAL_EQ_RDIV_EQ" > "HOL4Real.real.REAL_EQ_RDIV_EQ"
-  "REAL_EQ_RADD" > "Ring_and_Field.add_right_cancel"
-  "REAL_EQ_NEG" > "Ring_and_Field.neg_equal_iff_equal"
+  "REAL_EQ_RADD" > "OrderedGroup.add_right_cancel"
+  "REAL_EQ_NEG" > "OrderedGroup.neg_equal_iff_equal"
   "REAL_EQ_MUL_LCANCEL" > "Ring_and_Field.field_mult_cancel_left"
   "REAL_EQ_LMUL_IMP" > "HOL4Real.real.REAL_EQ_LMUL_IMP"
   "REAL_EQ_LMUL2" > "RealDef.real_mult_left_cancel"
   "REAL_EQ_LMUL" > "Ring_and_Field.field_mult_cancel_left"
   "REAL_EQ_LDIV_EQ" > "HOL4Real.real.REAL_EQ_LDIV_EQ"
-  "REAL_EQ_LADD" > "Ring_and_Field.add_left_cancel"
+  "REAL_EQ_LADD" > "OrderedGroup.add_left_cancel"
   "REAL_EQ_IMP_LE" > "HOL.order_eq_refl"
   "REAL_ENTIRE" > "Ring_and_Field.field_mult_eq_0_iff"
   "REAL_DOWN2" > "RealDef.real_lbound_gt_zero"
@@ -285,22 +285,22 @@
   "REAL_ARCH" > "RComplete.reals_Archimedean3"
   "REAL_ADD_SYM" > "Ring_and_Field.ring_eq_simps_9"
   "REAL_ADD_SUB2" > "HOL4Real.real.REAL_ADD_SUB2"
-  "REAL_ADD_SUB" > "Ring_and_Field.add_minus_self_right"
-  "REAL_ADD_RINV" > "Ring_and_Field.right_minus"
+  "REAL_ADD_SUB" > "HOL4Real.real.REAL_ADD_SUB"
+  "REAL_ADD_RINV" > "OrderedGroup.right_minus"
   "REAL_ADD_RID_UNIQ" > "HOL4Real.real.REAL_ADD_RID_UNIQ"
-  "REAL_ADD_RID" > "Ring_and_Field.add_0_right"
+  "REAL_ADD_RID" > "OrderedGroup.add_0_right"
   "REAL_ADD_RDISTRIB" > "Ring_and_Field.ring_eq_simps_4"
   "REAL_ADD_LINV" > "HOL4Compat.REAL_ADD_LINV"
   "REAL_ADD_LID_UNIQ" > "HOL4Real.real.REAL_ADD_LID_UNIQ"
-  "REAL_ADD_LID" > "Ring_and_Field.abelian_semigroup.add_0"
+  "REAL_ADD_LID" > "OrderedGroup.comm_monoid_add.add_0"
   "REAL_ADD_LDISTRIB" > "Ring_and_Field.ring_eq_simps_5"
   "REAL_ADD_ASSOC" > "HOL4Compat.REAL_ADD_ASSOC"
   "REAL_ADD2_SUB2" > "HOL4Real.real.REAL_ADD2_SUB2"
   "REAL_ADD" > "RealDef.real_of_nat_add"
-  "REAL_ABS_TRIANGLE" > "Ring_and_Field.abs_triangle_ineq"
-  "REAL_ABS_POS" > "Ring_and_Field.abs_ge_zero"
+  "REAL_ABS_TRIANGLE" > "OrderedGroup.abs_triangle_ineq"
+  "REAL_ABS_POS" > "OrderedGroup.abs_ge_zero"
   "REAL_ABS_MUL" > "Ring_and_Field.abs_mult"
-  "REAL_ABS_0" > "Ring_and_Field.abs_zero"
+  "REAL_ABS_0" > "OrderedGroup.abs_zero"
   "REAL_10" > "HOL4Compat.REAL_10"
   "REAL_1" > "HOL4Real.real.REAL_1"
   "REAL_0" > "HOL4Real.real.REAL_0"
@@ -326,8 +326,8 @@
   "POW_2" > "NatBin.power2_eq_square"
   "POW_1" > "Power.power_one_right"
   "POW_0" > "Power.power_0_Suc"
-  "ABS_ZERO" > "Ring_and_Field.abs_zero_iff"
-  "ABS_TRIANGLE" > "Ring_and_Field.abs_triangle_ineq"
+  "ABS_ZERO" > "OrderedGroup.abs_eq_0"
+  "ABS_TRIANGLE" > "OrderedGroup.abs_triangle_ineq"
   "ABS_SUM" > "HOL4Real.real.ABS_SUM"
   "ABS_SUB_ABS" > "HOL4Real.real.ABS_SUB_ABS"
   "ABS_SUB" > "HOL4Real.real.ABS_SUB"
@@ -336,13 +336,13 @@
   "ABS_SIGN" > "HOL4Real.real.ABS_SIGN"
   "ABS_REFL" > "HOL4Real.real.ABS_REFL"
   "ABS_POW2" > "NatBin.abs_power2"
-  "ABS_POS" > "Ring_and_Field.abs_ge_zero"
-  "ABS_NZ" > "Ring_and_Field.zero_less_abs_iff"
-  "ABS_NEG" > "Ring_and_Field.abs_minus_cancel"
+  "ABS_POS" > "OrderedGroup.abs_ge_zero"
+  "ABS_NZ" > "OrderedGroup.zero_less_abs_iff"
+  "ABS_NEG" > "OrderedGroup.abs_minus_cancel"
   "ABS_N" > "RealDef.abs_real_of_nat_cancel"
   "ABS_MUL" > "Ring_and_Field.abs_mult"
   "ABS_LT_MUL2" > "HOL4Real.real.ABS_LT_MUL2"
-  "ABS_LE" > "Ring_and_Field.abs_ge_self"
+  "ABS_LE" > "OrderedGroup.abs_ge_self"
   "ABS_INV" > "Ring_and_Field.nonzero_abs_inverse"
   "ABS_DIV" > "Ring_and_Field.nonzero_abs_divide"
   "ABS_CIRCLE" > "HOL4Real.real.ABS_CIRCLE"
@@ -352,8 +352,8 @@
   "ABS_BETWEEN2" > "HOL4Real.real.ABS_BETWEEN2"
   "ABS_BETWEEN1" > "HOL4Real.real.ABS_BETWEEN1"
   "ABS_BETWEEN" > "HOL4Real.real.ABS_BETWEEN"
-  "ABS_ABS" > "Ring_and_Field.abs_idempotent"
+  "ABS_ABS" > "OrderedGroup.abs_idempotent"
   "ABS_1" > "Ring_and_Field.abs_one"
-  "ABS_0" > "Ring_and_Field.abs_zero"
+  "ABS_0" > "OrderedGroup.abs_zero"
 
 end

--- a/src/HOL/Import/HOL/realax.imp	Fri May 21 21:28:58 2004 +0200
+++ b/src/HOL/Import/HOL/realax.imp	Fri May 21 21:42:05 2004 +0200
@@ -93,18 +93,18 @@
   "REAL_SUP_ALLPOS" > "HOL4Compat.REAL_SUP_ALLPOS"
   "REAL_MUL_SYM" > "Ring_and_Field.ring_eq_simps_2"
   "REAL_MUL_LINV" > "HOL4Compat.REAL_MUL_LINV"
-  "REAL_MUL_LID" > "Ring_and_Field.almost_semiring.mult_1"
+  "REAL_MUL_LID" > "OrderedGroup.comm_monoid_mult.mult_1"
   "REAL_MUL_ASSOC" > "HOL4Compat.REAL_MUL_ASSOC"
   "REAL_LT_TRANS" > "Set.basic_trans_rules_21"
   "REAL_LT_TOTAL" > "HOL4Compat.REAL_LT_TOTAL"
   "REAL_LT_REFL" > "HOL.order_less_irrefl"
   "REAL_LT_MUL" > "Ring_and_Field.mult_pos"
-  "REAL_LT_IADD" > "Ring_and_Field.add_strict_left_mono"
+  "REAL_LT_IADD" > "OrderedGroup.add_strict_left_mono"
   "REAL_LDISTRIB" > "Ring_and_Field.ring_eq_simps_5"
   "REAL_INV_0" > "Ring_and_Field.division_by_zero.inverse_zero"
   "REAL_ADD_SYM" > "Ring_and_Field.ring_eq_simps_9"
   "REAL_ADD_LINV" > "HOL4Compat.REAL_ADD_LINV"
-  "REAL_ADD_LID" > "Ring_and_Field.abelian_semigroup.add_0"
+  "REAL_ADD_LID" > "OrderedGroup.comm_monoid_add.add_0"
   "REAL_ADD_ASSOC" > "HOL4Compat.REAL_ADD_ASSOC"
   "REAL_10" > "HOL4Compat.REAL_10"
   "HREAL_RDISTRIB" > "HOL4Real.realax.HREAL_RDISTRIB"