theorem Th18:
  F |^ 0 = id S
proof
  set G=GFuncs the carrier of S;
  reconsider F9=F as Element of G by MONOID_0:73;
  0|->F9=<*>the carrier of G;
  then Product(0|->F9) = 1_G by GROUP_4:8
    .= the_unity_wrt the multF of G by GROUP_1:22
    .= id S by MONOID_0:75;
  hence thesis by Def4;
end;
