equal
deleted
inserted
replaced
30 definition |
30 definition |
31 trans :: "i\<Rightarrow>o" where |
31 trans :: "i\<Rightarrow>o" where |
32 "trans(r) \<equiv> \<forall>x y z. \<langle>x,y\<rangle>: r \<longrightarrow> \<langle>y,z\<rangle>: r \<longrightarrow> \<langle>x,z\<rangle>: r" |
32 "trans(r) \<equiv> \<forall>x y z. \<langle>x,y\<rangle>: r \<longrightarrow> \<langle>y,z\<rangle>: r \<longrightarrow> \<langle>x,z\<rangle>: r" |
33 |
33 |
34 definition |
34 definition |
35 trans_on :: "[i,i]\<Rightarrow>o" (\<open>trans[_]'(_')\<close>) where |
35 trans_on :: "[i,i]\<Rightarrow>o" (\<open>(\<open>open_block notation=\<open>mixfix trans_on\<close>\<close>trans[_]'(_'))\<close>) where |
36 "trans[A](r) \<equiv> \<forall>x\<in>A. \<forall>y\<in>A. \<forall>z\<in>A. |
36 "trans[A](r) \<equiv> \<forall>x\<in>A. \<forall>y\<in>A. \<forall>z\<in>A. |
37 \<langle>x,y\<rangle>: r \<longrightarrow> \<langle>y,z\<rangle>: r \<longrightarrow> \<langle>x,z\<rangle>: r" |
37 \<langle>x,y\<rangle>: r \<longrightarrow> \<langle>y,z\<rangle>: r \<longrightarrow> \<langle>x,z\<rangle>: r" |
38 |
38 |
39 definition |
39 definition |
40 rtrancl :: "i\<Rightarrow>i" (\<open>(\<open>notation=\<open>postfix ^*\<close>\<close>_^*)\<close> [100] 100) (*refl/transitive closure*) where |
40 rtrancl :: "i\<Rightarrow>i" (\<open>(\<open>notation=\<open>postfix ^*\<close>\<close>_^*)\<close> [100] 100) (*refl/transitive closure*) where |