let D', E, D be non empty set ; :: thesis: for d being Element of D
for i being Nat
for F being Function of [:D,D':],E
for T being Tuple of i, holds F .: T,(i |-> d) = F [:] T,d
let d be Element of D; :: thesis: for i being Nat
for F being Function of [:D,D':],E
for T being Tuple of i, holds F .: T,(i |-> d) = F [:] T,d
let i be Nat; :: thesis: for F being Function of [:D,D':],E
for T being Tuple of i, holds F .: T,(i |-> d) = F [:] T,d
let F be Function of [:D,D':],E; :: thesis: for T being Tuple of i, holds F .: T,(i |-> d) = F [:] T,d
let T be Tuple of i, ; :: thesis: F .: T,(i |-> d) = F [:] T,d
dom T = Seg (len T) by FINSEQ_1:def 3
.= Seg i by FINSEQ_1:def 18 ;
hence F .: T,(i |-> d) = F [:] T,d ; :: thesis: verum