src/ZF/Trancl.thy
changeset 81125 ec121999a9cb
parent 80917 2a77bc3b4eac
equal deleted inserted replaced
81124:6ce0c8d59f5a 81125:ec121999a9cb
    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