reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  i in dom f & f is one-to-one implies f/.i..f = i
proof
  assume
A1: i in dom f;
  assume f is one-to-one;
  then (f.i)..f = i by A1,Th11;
  hence thesis by A1,PARTFUN1:def 6;
end;
