
theorem
for R being 0-characteristic Ring holds Frob R = (the carrier of R) --> 1.R
proof
let R be 0-characteristic Ring;
I: Char R = 0 by RING_3:def 6;
now let o be object;
  assume A: o in the carrier of R;
  then reconsider a = o as Element of R;
  thus (Frob R).o = a|^0 by I,defFr
                 .= 1_R by BINOM:8
                 .= ((the carrier of R) --> 1.R).o by A,FUNCOP_1:7;
  end;
hence thesis;
end;
