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_1:79
.= (F [:] (id D),d) * T by FUNCOP_1:37 ;
:: thesis: verum