let D, D', E be non empty set ; :: thesis: for d1, d2, d3 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,d3*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*>
let d1, d2, d3 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,d3*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,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,d3*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*>
let F be Function of [:D,D':],E; :: thesis: for p being FinSequence of D st p = <*d1,d2,d3*> holds
F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*>
let p be FinSequence of D; :: thesis: ( p = <*d1,d2,d3*> implies F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*> )
assume A1: p = <*d1,d2,d3*> ; :: thesis: F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*>
reconsider r = F [:] p,d' as FinSequence of E by Th97;
len p = 3 by A1, FINSEQ_1:62;
then A2: len r = 3 by Th98;
then ( 1 in Seg (len r) & 2 in Seg (len r) & 3 in Seg (len r) ) ;
then ( 1 in dom r & 2 in dom r & 3 in dom r & p . 1 = d1 & p . 2 = d2 & p . 3 = d3 ) by A1, FINSEQ_1:62, FINSEQ_1:def 3;
then ( r . 1 = F . d1,d' & r . 2 = F . d2,d' & r . 3 = F . d3,d' ) by FUNCOP_1:35;
hence F [:] p,d' = <*(F . d1,d'),(F . d2,d'),(F . d3,d')*> by A2, FINSEQ_1:62; :: thesis: verum