Dear Adem, you have no chance to prove the existence of the definition
definition
let o be real number, fs be FinSequence;
assume TAS: 1 <= len fs;
func distr(o,fs) -> FinSequence means
dom it = Seg(len fs) &
it.1 = S &
for i being Nat st i in Seg(len fs)\{1} holds
ex p being FinSequence st p = fs.i & it.i = sexp(o,p);
The problem is that loci 'fs' must be 'FinSequence-yielding' to ensure that 'fs.i' is a FinSequence.
Look at: definition let IT be Function; attr IT is FinSequence-yielding means :: PRE_POLY:def 3 for x st x in dom IT holds IT.x is FinSequence; end; Best Artur