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 [;] d,p 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 [;] d,p 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 [;] d,p holds
len r = len p
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D' st r = F [;] d,p holds
len r = len p
let p be FinSequence of D'; :: thesis: ( r = F [;] d,p implies len r = len p )
( {d} c= D & rng p c= D' ) by FINSEQ_1:def 4;
then [:{d},(rng p):] c= [:D,D':] by ZFMISC_1:119;
then [:{d},(rng p):] c= dom F by FUNCT_2:def 1;
hence ( r = F [;] d,p implies len r = len p ) by Th81; :: thesis: verum