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

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