let D, D', E be non empty set ; :: thesis: for d being Element of D
for d' being Element of D'
for i being Nat
for F being Function of [:D,D':],E holds F [;] d,(i |-> d') = i |-> (F . d,d')
let d be Element of D; :: thesis: for d' being Element of D'
for i being Nat
for F being Function of [:D,D':],E holds F [;] d,(i |-> d') = i |-> (F . d,d')
let d' be Element of D'; :: thesis: for i being Nat
for F being Function of [:D,D':],E holds F [;] d,(i |-> d') = i |-> (F . d,d')
let i be Nat; :: thesis: for F being Function of [:D,D':],E holds F [;] d,(i |-> d') = i |-> (F . d,d')
let F be Function of [:D,D':],E; :: thesis: F [;] d,(i |-> d') = i |-> (F . d,d')
thus F [;] d,(i |-> d') = F .: (i |-> d),(i |-> d') by FUNCOP_1:19
.= i |-> (F . d,d') by Th18 ; :: thesis: verum