--- a/src/HOL/Library/Char_ord.thy Wed Jan 02 15:14:15 2008 +0100
+++ b/src/HOL/Library/Char_ord.thy Wed Jan 02 15:14:17 2008 +0100
@@ -9,10 +9,16 @@
imports Product_ord Char_nat
begin
-instance nibble :: linorder
- nibble_less_eq_def: "n \<le> m \<equiv> nat_of_nibble n \<le> nat_of_nibble m"
- nibble_less_def: "n < m \<equiv> nat_of_nibble n < nat_of_nibble m"
-proof
+instantiation nibble :: linorder
+begin
+
+definition
+ nibble_less_eq_def: "n \<le> m \<longleftrightarrow> nat_of_nibble n \<le> nat_of_nibble m"
+
+definition
+ nibble_less_def: "n < m \<longleftrightarrow> nat_of_nibble n < nat_of_nibble m"
+
+instance proof
fix n :: nibble
show "n \<le> n" unfolding nibble_less_eq_def nibble_less_def by auto
next
@@ -38,27 +44,52 @@
unfolding nibble_less_eq_def by auto
qed
-instance nibble :: distrib_lattice
+end
+
+instantiation nibble :: distrib_lattice
+begin
+
+definition
"(inf \<Colon> nibble \<Rightarrow> _) = min"
+
+definition
"(sup \<Colon> nibble \<Rightarrow> _) = max"
- by default (auto simp add:
+
+instance by default (auto simp add:
inf_nibble_def sup_nibble_def min_max.sup_inf_distrib1)
-instance char :: linorder
- char_less_eq_def: "c1 \<le> c2 \<equiv> case c1 of Char n1 m1 \<Rightarrow> case c2 of Char n2 m2 \<Rightarrow>
- n1 < n2 \<or> n1 = n2 \<and> m1 \<le> m2"
- char_less_def: "c1 < c2 \<equiv> case c1 of Char n1 m1 \<Rightarrow> case c2 of Char n2 m2 \<Rightarrow>
- n1 < n2 \<or> n1 = n2 \<and> m1 < m2"
+end
+
+instantiation char :: linorder
+begin
+
+definition
+ char_less_eq_def [code func del]: "c1 \<le> c2 \<longleftrightarrow> (case c1 of Char n1 m1 \<Rightarrow> case c2 of Char n2 m2 \<Rightarrow>
+ n1 < n2 \<or> n1 = n2 \<and> m1 \<le> m2)"
+
+definition
+ char_less_def [code func del]: "c1 < c2 \<longleftrightarrow> (case c1 of Char n1 m1 \<Rightarrow> case c2 of Char n2 m2 \<Rightarrow>
+ n1 < n2 \<or> n1 = n2 \<and> m1 < m2)"
+
+instance
by default (auto simp: char_less_eq_def char_less_def split: char.splits)
-lemmas [code func del] = char_less_eq_def char_less_def
+end
-instance char :: distrib_lattice
+instantiation char :: distrib_lattice
+begin
+
+definition
"(inf \<Colon> char \<Rightarrow> _) = min"
+
+definition
"(sup \<Colon> char \<Rightarrow> _) = max"
- by default (auto simp add:
+
+instance by default (auto simp add:
inf_char_def sup_char_def min_max.sup_inf_distrib1)
+end
+
lemma [simp, code func]:
shows char_less_eq_simp: "Char n1 m1 \<le> Char n2 m2 \<longleftrightarrow> n1 < n2 \<or> n1 = n2 \<and> m1 \<le> m2"
and char_less_simp: "Char n1 m1 < Char n2 m2 \<longleftrightarrow> n1 < n2 \<or> n1 = n2 \<and> m1 < m2"