let D, D9, E be non empty set ; 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; 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; 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; for p being FinSequence of D9 st r = F [;] (d,p) holds
len r = len p
let p be FinSequence of D9; ( 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; verum