reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th13:
  i in dom p implies i in dom(p^q)
proof
A1: dom p c= dom(p^q) by FINSEQ_1:26;
  assume i in dom p;
  hence thesis by A1;
end;
