reserve i,j,k,n for Nat;

theorem Th11:
  for f being one-to-one FinSequence st i in dom f holds (f.i)..f = i
proof
  let f be one-to-one FinSequence;
  assume
A1: i in dom f;
  then f.i in rng f by FUNCT_1:def 3;
  then
A2: f just_once_values f.i by FINSEQ_4:8;
  then f <- (f.i) = (f.i)..f by FINSEQ_4:25;
  hence thesis by A1,A2,FINSEQ_4:def 3;
end;
