let D, E, D9 be non empty set ; :: thesis: for d being Element of D
for i being Nat
for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F .: ((i |-> d),T9) = F [;] (d,T9)
let d be Element of D; :: thesis: for i being Nat
for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F .: ((i |-> d),T9) = F [;] (d,T9)
let i be Nat; :: thesis: for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F .: ((i |-> d),T9) = F [;] (d,T9)
let F be Function of [:D,D9:],E; :: thesis: for T9 being Tuple of i,D9 holds F .: ((i |-> d),T9) = F [;] (d,T9)
let T9 be Tuple of i,D9; :: thesis: F .: ((i |-> d),T9) = F [;] (d,T9)
dom T9 = Seg (len T9) by FINSEQ_1:def 3
.= Seg i by CARD_1:def 7 ;
hence F .: ((i |-> d),T9) = F [;] (d,T9) ; :: thesis: verum