reserve k,m,n for Nat,
  i1,i2,i3 for Integer,
  e for set;
reserve i,k,m,n,p,x,y for Nat;
reserve a for Tuple of n,(k-SD);

theorem Th15:
  i in Seg n implies DigA(a,i) is Element of k-SD
proof
  assume
A1: i in Seg n;
  then a.i = DigA(a,i) by Def3;
  hence thesis by A1,Th14;
end;
