
theorem
  for D being non empty set,f being FinSequence of D holds f is_terminated_by f
proof
  let D be non empty set,f be FinSequence of D;
A1: len f + 1 -'len f=len f+1-len f by XREAL_0:def 2;
  1-'1=0+1-'1 .=0 by NAT_D:34;
  then
A2: f/^(1-'1)=f by FINSEQ_5:28;
  for j being Element of NAT st j >= 1 & j > 0
  & f is_preposition_of f/^(j-'1) holds j >= 1;
  hence thesis by A1,A2,Def10;
end;
