let D, D9, E be non empty set ; :: thesis: for d9 being Element of D9
for r being FinSequence
for F being Function of [:D,D9:],E
for p being FinSequence of D st r = F [:] (p,d9) holds
len r = len p
let d9 be Element of D9; :: thesis: for r being FinSequence
for F being Function of [:D,D9:],E
for p being FinSequence of D st r = F [:] (p,d9) holds
len r = len p
let r be FinSequence; :: thesis: for F being Function of [:D,D9:],E
for p being FinSequence of D st r = F [:] (p,d9) holds
len r = len p
let F be Function of [:D,D9:],E; :: thesis: for p being FinSequence of D st r = F [:] (p,d9) holds
len r = len p
let p be FinSequence of D; :: thesis: ( r = F [:] (p,d9) implies len r = len p )
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;
hence ( r = F [:] (p,d9) implies len r = len p ) by Th67; :: thesis: verum