--- a/src/HOL/Library/Abstract_Rat.thy Sat Aug 29 14:31:39 2009 +0200
+++ b/src/HOL/Library/Abstract_Rat.thy Mon Aug 31 14:09:42 2009 +0200
@@ -189,14 +189,9 @@
have "\<exists> a b a' b'. x = (a,b) \<and> y = (a',b')" by auto
then obtain a b a' b' where xy[simp]: "x = (a,b)" "y=(a',b')" by blast
assume H: ?lhs
- {assume "a = 0 \<or> b = 0 \<or> a' = 0 \<or> b' = 0" hence ?rhs
- using na nb H
- apply (simp add: INum_def split_def isnormNum_def)
- apply (cases "a = 0", simp_all)
- apply (cases "b = 0", simp_all)
- apply (cases "a' = 0", simp_all)
- apply (cases "a' = 0", simp_all add: of_int_eq_0_iff)
- done}
+ {assume "a = 0 \<or> b = 0 \<or> a' = 0 \<or> b' = 0"
+ hence ?rhs using na nb H
+ by (simp add: INum_def split_def isnormNum_def split: split_if_asm)}
moreover
{ assume az: "a \<noteq> 0" and bz: "b \<noteq> 0" and a'z: "a'\<noteq>0" and b'z: "b'\<noteq>0"
from az bz a'z b'z na nb have pos: "b > 0" "b' > 0" by (simp_all add: isnormNum_def)
@@ -517,10 +512,7 @@
have n0: "isnormNum 0\<^sub>N" by simp
show ?thesis using nx ny
apply (simp only: isnormNum_unique[where ?'a = 'a, OF Nmul_normN[OF nx ny] n0, symmetric] Nmul[where ?'a = 'a])
- apply (simp add: INum_def split_def isnormNum_def fst_conv snd_conv)
- apply (cases "a=0",simp_all)
- apply (cases "a'=0",simp_all)
- done
+ by (simp add: INum_def split_def isnormNum_def fst_conv snd_conv split: split_if_asm)
}
qed
lemma Nneg_Nneg[simp]: "~\<^sub>N (~\<^sub>N c) = c"