reserve N for Cardinal;
reserve M for Aleph;
reserve X for non empty set;
reserve Y,Z,Z1,Z2,Y1,Y2,Y3,Y4 for Subset of X;
reserve S for Subset-Family of X;
reserve x for set;
reserve F,Uf for Filter of X;
reserve S for non empty Subset-Family of X;
reserve I for Ideal of X;
reserve S,S1 for Subset-Family of X;
reserve FS for non empty Subset of Filters(X);
reserve X for infinite set;
reserve Y,Y1,Y2,Z for Subset of X;
reserve F,Uf for Filter of X;
reserve x for Element of X;
reserve X for set;
reserve M for non limit_cardinal Aleph;
reserve F for Filter of M;
reserve N1,N2,N3 for Element of predecessor M;
reserve K1,K2 for Element of M;
reserve T for Inf_Matrix of predecessor M, M, bool M;
reserve M for Aleph;

theorem Th38:
  M is measurable implies M is limit_cardinal
proof
  assume M is measurable;
  then consider F being Filter of M such that
A1: F is_complete_with M and
A2: F is non principal being_ultrafilter;
  assume
A3: not M is limit_cardinal;
  F is_complete_with card M by A1;
  hence contradiction by A2,A3,Th23,Th37;
end;
