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