--- a/src/HOL/Ring_and_Field.thy Thu Jul 10 07:07:54 2008 +0200
+++ b/src/HOL/Ring_and_Field.thy Thu Jul 10 07:15:19 2008 +0200
@@ -80,14 +80,14 @@
class comm_semiring_0 = comm_semiring + comm_monoid_add + mult_zero
begin
-subclass semiring_0 by intro_locales
+subclass semiring_0 ..
end
class comm_semiring_0_cancel = comm_semiring + comm_monoid_add + cancel_ab_semigroup_add
begin
-subclass semiring_0_cancel by intro_locales
+subclass semiring_0_cancel ..
end
@@ -106,7 +106,7 @@
(*previously almost_semiring*)
begin
-subclass semiring_1 by intro_locales
+subclass semiring_1 ..
end
@@ -117,9 +117,9 @@
+ cancel_ab_semigroup_add + monoid_mult
begin
-subclass semiring_0_cancel by intro_locales
+subclass semiring_0_cancel ..
-subclass semiring_1 by intro_locales
+subclass semiring_1 ..
end
@@ -127,16 +127,16 @@
+ zero_neq_one + cancel_ab_semigroup_add
begin
-subclass semiring_1_cancel by intro_locales
-subclass comm_semiring_0_cancel by intro_locales
-subclass comm_semiring_1 by intro_locales
+subclass semiring_1_cancel ..
+subclass comm_semiring_0_cancel ..
+subclass comm_semiring_1 ..
end
class ring = semiring + ab_group_add
begin
-subclass semiring_0_cancel by intro_locales
+subclass semiring_0_cancel ..
text {* Distribution rules *}
@@ -185,15 +185,15 @@
class comm_ring = comm_semiring + ab_group_add
begin
-subclass ring by intro_locales
-subclass comm_semiring_0 by intro_locales
+subclass ring ..
+subclass comm_semiring_0 ..
end
class ring_1 = ring + zero_neq_one + monoid_mult
begin
-subclass semiring_1_cancel by intro_locales
+subclass semiring_1_cancel ..
end
@@ -201,8 +201,8 @@
(*previously ring*)
begin
-subclass ring_1 by intro_locales
-subclass comm_semiring_1_cancel by intro_locales
+subclass ring_1 ..
+subclass comm_semiring_1_cancel ..
end
@@ -263,7 +263,7 @@
class idom = comm_ring_1 + no_zero_divisors
begin
-subclass ring_1_no_zero_divisors by intro_locales
+subclass ring_1_no_zero_divisors ..
end
@@ -394,7 +394,7 @@
thus "a * inverse a = 1" by (simp only: mult_commute)
qed
-subclass idom by intro_locales
+subclass idom ..
lemma right_inverse_eq: "b \<noteq> 0 \<Longrightarrow> a / b = 1 \<longleftrightarrow> a = b"
proof
@@ -464,8 +464,8 @@
+ semiring + comm_monoid_add + cancel_ab_semigroup_add
begin
-subclass semiring_0_cancel by intro_locales
-subclass pordered_semiring by intro_locales
+subclass semiring_0_cancel ..
+subclass pordered_semiring ..
lemma mult_nonneg_nonneg: "0 \<le> a \<Longrightarrow> 0 \<le> b \<Longrightarrow> 0 \<le> a * b"
by (drule mult_left_mono [of zero b], auto)
@@ -484,9 +484,9 @@
class ordered_semiring = semiring + comm_monoid_add + ordered_cancel_ab_semigroup_add + mult_mono
begin
-subclass pordered_cancel_semiring by intro_locales
+subclass pordered_cancel_semiring ..
-subclass pordered_comm_monoid_add by intro_locales
+subclass pordered_comm_monoid_add ..
lemma mult_left_less_imp_less:
"c * a < c * b \<Longrightarrow> 0 \<le> c \<Longrightarrow> a < b"
@@ -503,7 +503,7 @@
assumes mult_strict_right_mono: "a < b \<Longrightarrow> 0 < c \<Longrightarrow> a * c < b * c"
begin
-subclass semiring_0_cancel by intro_locales
+subclass semiring_0_cancel ..
subclass ordered_semiring
proof unfold_locales
@@ -637,8 +637,8 @@
+ pordered_ab_semigroup_add + mult_mono1
begin
-subclass pordered_comm_semiring by intro_locales
-subclass pordered_cancel_semiring by intro_locales
+subclass pordered_comm_semiring ..
+subclass pordered_cancel_semiring ..
end
@@ -668,7 +668,7 @@
class pordered_ring = ring + pordered_cancel_semiring
begin
-subclass pordered_ab_group_add by intro_locales
+subclass pordered_ab_group_add ..
lemmas ring_simps = ring_simps group_simps
@@ -723,7 +723,7 @@
+ ordered_ab_group_add + abs_if
begin
-subclass pordered_ring by intro_locales
+subclass pordered_ring ..
subclass pordered_ab_group_add_abs
proof unfold_locales
@@ -744,7 +744,7 @@
+ ordered_ab_group_add + abs_if
begin
-subclass ordered_ring by intro_locales
+subclass ordered_ring ..
lemma mult_strict_left_mono_neg:
"b < a \<Longrightarrow> c < 0 \<Longrightarrow> c * a < c * b"
@@ -888,8 +888,8 @@
class pordered_comm_ring = comm_ring + pordered_comm_semiring
begin
-subclass pordered_ring by intro_locales
-subclass pordered_cancel_comm_semiring by intro_locales
+subclass pordered_ring ..
+subclass pordered_cancel_comm_semiring ..
end
@@ -925,9 +925,9 @@
(*previously ordered_ring*)
begin
-subclass ordered_ring_strict by intro_locales
-subclass pordered_comm_ring by intro_locales
-subclass idom by intro_locales
+subclass ordered_ring_strict ..
+subclass pordered_comm_ring ..
+subclass idom ..
subclass ordered_semidom
proof unfold_locales
@@ -1983,8 +1983,8 @@
class lordered_ring = pordered_ring + lordered_ab_group_add_abs
begin
-subclass lordered_ab_group_add_meet by intro_locales
-subclass lordered_ab_group_add_join by intro_locales
+subclass lordered_ab_group_add_meet ..
+subclass lordered_ab_group_add_join ..
end