theorem
  for H being strict Subgroup of G holds
  con_class H is finite or Left_Cosets Normalizer H is finite implies
  ex C being finite set st
  C = con_class H & card C = index Normalizer H
proof
  let H be strict Subgroup of G;
A1: card con_class H = Index Normalizer H by Th135
    .= card Left_Cosets Normalizer H;
  assume
A3: con_class H is finite or Left_Cosets Normalizer H is finite;
  then reconsider C = con_class H as finite set by A1;
  take C;
  thus C = con_class H;
  Left_Cosets Normalizer H is finite by A3,A1;
  hence thesis by A1,Def18;
end;
