reserve i,n,m,k,x for Nat,
  i1,i2 for Integer;
reserve a for Tuple of n,k-SD;
reserve aSub for Tuple of n,k-SD_Sub;

theorem Th11:
  i in Seg n implies aSub.i is Element of k-SD_Sub
proof
A1: len aSub = n by CARD_1:def 7;
  assume i in Seg n;
  then i in dom aSub by A1,FINSEQ_1:def 3;
  then
A2: aSub.i in rng aSub by FUNCT_1:def 3;
  rng aSub c= k-SD_Sub by FINSEQ_1:def 4;
  hence thesis by A2;
end;
