let x1 be set ; :: thesis: for D, D' being non empty set
for p being FinSequence of D
for f being Function of D,D' st p = <*x1*> holds
f * p = <*(f . x1)*>
let D, D' be non empty set ; :: thesis: for p being FinSequence of D
for f being Function of D,D' st p = <*x1*> holds
f * p = <*(f . x1)*>
let p be FinSequence of D; :: thesis: for f being Function of D,D' st p = <*x1*> holds
f * p = <*(f . x1)*>
let f be Function of D,D'; :: thesis: ( p = <*x1*> implies f * p = <*(f . x1)*> )
assume A1: p = <*x1*> ; :: thesis: f * p = <*(f . x1)*>
reconsider q = f * p as FinSequence of D' by Th36;
len p = 1 by A1, FINSEQ_1:56;
then A2: len q = 1 by Th37;
then 1 in Seg (len q) ;
then ( 1 in dom q & p . 1 = x1 ) by A1, FINSEQ_1:57, FINSEQ_1:def 3;
then q . 1 = f . x1 by FUNCT_1:22;
hence f * p = <*(f . x1)*> by A2, FINSEQ_1:57; :: thesis: verum