let a be object ; :: thesis: for p, r being FinSequence
for F being Function st [:{a},(rng p):] c= dom F & r = F [;] (a,p) holds
len r = len p
let p, r be FinSequence; :: thesis: for F being Function st [:{a},(rng p):] c= dom F & r = F [;] (a,p) holds
len r = len p
let F be Function; :: thesis: ( [:{a},(rng p):] c= dom F & r = F [;] (a,p) implies len r = len p )
assume [:{a},(rng p):] c= dom F ; :: thesis: ( not r = F [;] (a,p) or len r = len p )
then dom (F [;] (a,p)) = dom p by Lm4;
then dom (F [;] (a,p)) = Seg (len p) by FINSEQ_1:def 3;
hence ( not r = F [;] (a,p) or len r = len p ) by FINSEQ_1:def 3; :: thesis: verum