let D, D', E be non empty set ; :: thesis: for r being FinSequence
for F being Function of [:D,D':],E
for p being FinSequence of D
for q being FinSequence of D' st r = F .: p,q holds
len r = min (len p),(len q)
let r be FinSequence; :: thesis: for F being Function of [:D,D':],E
for p being FinSequence of D
for q being FinSequence of D' st r = F .: p,q holds
len r = min (len p),(len q)
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D
for q being FinSequence of D' st r = F .: p,q holds
len r = min (len p),(len q)
let p be FinSequence of D; :: thesis: for q being FinSequence of D' st r = F .: p,q holds
len r = min (len p),(len q)
let q be FinSequence of D'; :: thesis: ( r = F .: p,q implies len r = min (len p),(len q) )
( rng p c= D & rng q c= D' ) by FINSEQ_1:def 4;
then [:(rng p),(rng q):] c= [:D,D':] by ZFMISC_1:119;
then [:(rng p),(rng q):] c= dom F by FUNCT_2:def 1;
hence ( r = F .: p,q implies len r = min (len p),(len q) ) by Th79; :: thesis: verum