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