let D, D9, E be non empty set ; :: thesis: for r being FinSequence
for F being Function of [:D,D9:],E
for p being FinSequence of D
for q being FinSequence of D9 st r = F .: (p,q) holds
len r = min ((len p),(len q))
let r be FinSequence; :: thesis: for F being Function of [:D,D9:],E
for p being FinSequence of D
for q being FinSequence of D9 st r = F .: (p,q) holds
len r = min ((len p),(len q))
let F be Function of [:D,D9:],E; :: thesis: for p being FinSequence of D
for q being FinSequence of D9 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 D9 st r = F .: (p,q) holds
len r = min ((len p),(len q))
let q be FinSequence of D9; :: thesis: ( r = F .: (p,q) implies len r = min ((len p),(len q)) )
( rng p c= D & rng q c= D9 ) by FINSEQ_1:def 4;
then [:(rng p),(rng q):] c= [:D,D9:] by ZFMISC_1:96;
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