let D, D9, E be non empty set ; :: thesis: for d being Element of D
for r being FinSequence
for F being Function of [:D,D9:],E
for p being FinSequence of D9 st r = F [;] (d,p) holds
len r = len p
let d be Element of D; :: thesis: for r being FinSequence
for F being Function of [:D,D9:],E
for p being FinSequence of D9 st r = F [;] (d,p) holds
len r = len p
let r be FinSequence; :: thesis: for F being Function of [:D,D9:],E
for p being FinSequence of D9 st r = F [;] (d,p) holds
len r = len p
let F be Function of [:D,D9:],E; :: thesis: for p being FinSequence of D9 st r = F [;] (d,p) holds
len r = len p
let p be FinSequence of D9; :: thesis: ( r = F [;] (d,p) implies len r = len p )
rng p c= D9 by FINSEQ_1:def 4;
then [:{d},(rng p):] c= [:D,D9:] by ZFMISC_1:96;
then [:{d},(rng p):] c= dom F by FUNCT_2:def 1;
hence ( r = F [;] (d,p) implies len r = len p ) by Th65; :: thesis: verum