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 Th20:
  x in dom q implies ex k st k=x & len p + k in dom(p^q)
proof
  assume
A1: x in dom q;
  then reconsider k=x as Element of NAT;
  take k;
  len p + k < len p + len q by XREAL_1:8,A1,Lm1;
  then len p + k in Segm(len p + len q) by NAT_1:44;
  hence thesis by Def3;
end;
