let a be set ; :: thesis: for p being FinSequence
for F being Function st [:(rng p),{a}:] c= dom F holds
F [:] p,a is FinSequence
let p be FinSequence; :: thesis: for F being Function st [:(rng p),{a}:] c= dom F holds
F [:] p,a is FinSequence
let F be Function; :: thesis: ( [:(rng p),{a}:] c= dom F implies F [:] p,a is FinSequence )
assume [:(rng p),{a}:] c= dom F ; :: thesis: F [:] p,a is FinSequence
then dom (F [:] p,a) = dom p by Lm5;
then dom (F [:] p,a) = Seg (len p) by FINSEQ_1:def 3;
hence F [:] p,a is FinSequence by FINSEQ_1:def 2; :: thesis: verum