let D, D', E be non empty set ; :: thesis: for d1, d2 being Element of D
for d1', d2' 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,d2*> & q = <*d1',d2'*> holds
F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
let d1, d2 be Element of D; :: thesis: for d1', d2' 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,d2*> & q = <*d1',d2'*> holds
F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
let d1', d2' 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,d2*> & q = <*d1',d2'*> holds
F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D
for q being FinSequence of D' st p = <*d1,d2*> & q = <*d1',d2'*> holds
F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
let p be FinSequence of D; :: thesis: for q being FinSequence of D' st p = <*d1,d2*> & q = <*d1',d2'*> holds
F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
let q be FinSequence of D'; :: thesis: ( p = <*d1,d2*> & q = <*d1',d2'*> implies F .: p,q = <*(F . d1,d1'),(F . d2,d2')*> )
assume A1: ( p = <*d1,d2*> & q = <*d1',d2'*> ) ; :: thesis: F .: p,q = <*(F . d1,d1'),(F . d2,d2')*>
reconsider r = F .: p,q as FinSequence of E by Th84;
( len p = 2 & len q = 2 ) by A1, FINSEQ_1:61;
then A2: len r = 2 by Th86;
then ( 1 in Seg (len r) & 2 in Seg (len r) ) ;
then ( 1 in dom r & 2 in dom r & p . 1 = d1 & q . 1 = d1' & p . 2 = d2 & q . 2 = d2' ) by A1, FINSEQ_1:61, FINSEQ_1:def 3;
then ( r . 1 = F . d1,d1' & r . 2 = F . d2,d2' ) by FUNCOP_1:28;
hence F .: p,q = <*(F . d1,d1'),(F . d2,d2')*> by A2, FINSEQ_1:61; :: thesis: verum