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
  for f being FinSequence st p in rng f holds (f-|p)^<*p*> = f|(p..f)
proof
  let f be FinSequence;
  assume
A1: p in rng f;
  then consider n being Nat such that
A2: n = p..f - 1 and
A3: f-|p = f | Seg n by FINSEQ_4:def 5;
  n+1 in dom f & f.(n+1) = p by A1,A2,FINSEQ_4:19,20;
  hence thesis by A2,A3,Th10;
end;
