let C be Category; :: thesis: for a, b being Object of C st a is initial holds
( dom (init a,b) = a & cod (init a,b) = b )
let a, b be Object of C; :: thesis: ( a is initial implies ( dom (init a,b) = a & cod (init a,b) = b ) )
assume a is initial ; :: thesis: ( dom (init a,b) = a & cod (init a,b) = b )
then Hom a,b <> {} by CAT_1:def 16;
hence ( dom (init a,b) = a & cod (init a,b) = b ) by CAT_1:23; :: thesis: verum