reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem
  len p = k + l & q = p | Seg k implies dom q = Seg k
proof
  assume that
A1: len p = k + l and
A2: q = p | Seg k;
  len q = k by A1,A2,Th51;
  hence thesis by FINSEQ_1:def 3;
end;
