let D, D', E be non empty set ; :: thesis: for d1, d2 being Element of D
for d' being Element of D'
for F being Function of [:D,D':],E
for p being FinSequence of D st p = <*d1,d2*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d')*>
let d1, d2 be Element of D; :: thesis: for d' being Element of D'
for F being Function of [:D,D':],E
for p being FinSequence of D st p = <*d1,d2*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d')*>
let d' be Element of D'; :: thesis: for F being Function of [:D,D':],E
for p being FinSequence of D st p = <*d1,d2*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d')*>
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D st p = <*d1,d2*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d')*>
let p be FinSequence of D; :: thesis: ( p = <*d1,d2*> implies F [:] p,d' = <*(F . d1,d'),(F . d2,d')*> )
assume A1: p = <*d1,d2*> ; :: thesis: F [:] p,d' = <*(F . d1,d'),(F . d2,d')*>
A2: p . 2 = d2 by A1, FINSEQ_1:61;
reconsider r = F [:] p,d' as FinSequence of E by Th97;
len p = 2 by A1, FINSEQ_1:61;
then A3: len r = 2 by Th98;
then 2 in Seg (len r) ;
then 2 in dom r by FINSEQ_1:def 3;
then A4: r . 2 = F . d2,d' by A2, FUNCOP_1:35;
1 in Seg (len r) by A3;
then A5: 1 in dom r by FINSEQ_1:def 3;
p . 1 = d1 by A1, FINSEQ_1:61;
then r . 1 = F . d1,d' by A5, FUNCOP_1:35;
hence F [:] p,d' = <*(F . d1,d'),(F . d2,d')*> by A3, A4, FINSEQ_1:61; :: thesis: verum