let D, D9, E be non empty set ; :: thesis: for d9 being Element of D9
for F being Function of [:D,D9:],E
for p being FinSequence of D holds F [:] (p,d9) is FinSequence of E
let d9 be Element of D9; :: thesis: for F being Function of [:D,D9:],E
for p being FinSequence of D holds F [:] (p,d9) is FinSequence of E
let F be Function of [:D,D9:],E; :: thesis: for p being FinSequence of D holds F [:] (p,d9) is FinSequence of E
let p be FinSequence of D; :: thesis: F [:] (p,d9) is FinSequence of E
A1: rng (F [:] (p,d9)) c= rng F by RELAT_1:26;
rng p c= D by FINSEQ_1:def 4;
then [:(rng p),{d9}:] c= [:D,D9:] by ZFMISC_1:96;
then [:(rng p),{d9}:] c= dom F by FUNCT_2:def 1;
then A2: F [:] (p,d9) is FinSequence by Th66;
rng F c= E by RELAT_1:def 19;
then rng (F [:] (p,d9)) c= E by A1;
hence F [:] (p,d9) is FinSequence of E by A2, FINSEQ_1:def 4; :: thesis: verum