equal
deleted
inserted
replaced
3004 by simp |
3004 by simp |
3005 |
3005 |
3006 lemma upt_conv_Cons: "i < j ==> [i..<j] = i # [Suc i..<j]" |
3006 lemma upt_conv_Cons: "i < j ==> [i..<j] = i # [Suc i..<j]" |
3007 by (simp add: upt_rec) |
3007 by (simp add: upt_rec) |
3008 |
3008 |
3009 lemma upt_conv_Cons_Cons: -- \<open>no precondition\<close> |
3009 lemma upt_conv_Cons_Cons: \<comment> \<open>no precondition\<close> |
3010 "m # n # ns = [m..<q] \<longleftrightarrow> n # ns = [Suc m..<q]" |
3010 "m # n # ns = [m..<q] \<longleftrightarrow> n # ns = [Suc m..<q]" |
3011 proof (cases "m < q") |
3011 proof (cases "m < q") |
3012 case False then show ?thesis by simp |
3012 case False then show ?thesis by simp |
3013 next |
3013 next |
3014 case True then show ?thesis by (simp add: upt_conv_Cons) |
3014 case True then show ?thesis by (simp add: upt_conv_Cons) |