theorem Th7:
  U0 is SubAlgebra of U1 implies dom the charact of(U0)=dom the charact of(U1)
proof
  assume
A1: U0 is SubAlgebra of U1;
  then reconsider A =the carrier of U0 as non empty Subset of U1 by Def7;
  the charact of(U0) = Opers(U1,A) by A1,Def7;
  hence thesis by Def6;
end;
