reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;

theorem Th16:
  len p <= k & k < len p + len q implies (p^q).k=q.(k-len p)
proof
  assume that
A1: len p <= k and
A2: k < len p + len q;
  consider m being Nat such that
A3: len p + m = k by A1,NAT_1:10;
  k - len p < len p + len q - len p by A2,XREAL_1:14;
  then m in dom q by A3,Lm1;
  hence thesis by A3,Def3;
end;
