let D, D', E be non empty set ; :: thesis: for d' being Element of D'
for r being FinSequence
for F being Function of [:D,D':],E
for p being FinSequence of D st r = F [:] p,d' holds
len r = len p
let d' be Element of D'; :: thesis: for r being FinSequence
for F being Function of [:D,D':],E
for p being FinSequence of D st r = F [:] p,d' holds
len r = len p
let r be FinSequence; :: thesis: for F being Function of [:D,D':],E
for p being FinSequence of D st r = F [:] p,d' holds
len r = len p
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D st r = F [:] p,d' holds
len r = len p
let p be FinSequence of D; :: thesis: ( r = F [:] p,d' implies len r = len p )
rng p c= D by FINSEQ_1:def 4;
then [:(rng p),{d'}:] c= [:D,D':] by ZFMISC_1:119;
then [:(rng p),{d'}:] c= dom F by FUNCT_2:def 1;
hence ( r = F [:] p,d' implies len r = len p ) by Th83; :: thesis: verum