let D, D', E be non empty set ; :: thesis: for d1 being Element of D
for d1' being Element of D'
for F being Function of [:D,D':],E
for p being FinSequence of D
for q being FinSequence of D' st p = <*d1*> & q = <*d1'*> holds
F .: p,q = <*(F . d1,d1')*>
let d1 be Element of D; :: thesis: for d1' being Element of D'
for F being Function of [:D,D':],E
for p being FinSequence of D
for q being FinSequence of D' st p = <*d1*> & q = <*d1'*> holds
F .: p,q = <*(F . d1,d1')*>
let d1' be Element of D'; :: thesis: for F being Function of [:D,D':],E
for p being FinSequence of D
for q being FinSequence of D' st p = <*d1*> & q = <*d1'*> holds
F .: p,q = <*(F . d1,d1')*>
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D
for q being FinSequence of D' st p = <*d1*> & q = <*d1'*> holds
F .: p,q = <*(F . d1,d1')*>
let p be FinSequence of D; :: thesis: for q being FinSequence of D' st p = <*d1*> & q = <*d1'*> holds
F .: p,q = <*(F . d1,d1')*>
let q be FinSequence of D'; :: thesis: ( p = <*d1*> & q = <*d1'*> implies F .: p,q = <*(F . d1,d1')*> )
assume A1: ( p = <*d1*> & q = <*d1'*> ) ; :: thesis: F .: p,q = <*(F . d1,d1')*>
reconsider r = F .: p,q as FinSequence of E by Th84;
( len p = 1 & len q = 1 ) by A1, FINSEQ_1:56;
then A2: len r = 1 by Th86;
then 1 in Seg (len r) ;
then ( 1 in dom r & p . 1 = d1 & q . 1 = d1' ) by A1, FINSEQ_1:57, FINSEQ_1:def 3;
then r . 1 = F . d1,d1' by FUNCOP_1:28;
hence F .: p,q = <*(F . d1,d1')*> by A2, FINSEQ_1:57; :: thesis: verum