let D9, E, D be non empty set ; :: thesis: for d being Element of D
for i being Nat
for F being Function of [:D,D9:],E
for T being Tuple of i,D holds F [:] (T,d) = (F [:] ((id D),d)) * T
let d be Element of D; :: thesis: for i being Nat
for F being Function of [:D,D9:],E
for T being Tuple of i,D holds F [:] (T,d) = (F [:] ((id D),d)) * T
let i be Nat; :: thesis: for F being Function of [:D,D9:],E
for T being Tuple of i,D holds F [:] (T,d) = (F [:] ((id D),d)) * T
let F be Function of [:D,D9:],E; :: thesis: for T being Tuple of i,D holds F [:] (T,d) = (F [:] ((id D),d)) * T
let T be Tuple of i,D; :: thesis: F [:] (T,d) = (F [:] ((id D),d)) * T
rng T c= D ;
hence F [:] (T,d) = F [:] (((id D) * T),d) by RELAT_1:53
.= (F [:] ((id D),d)) * T by FUNCOP_1:29 ;
:: thesis: verum