let D, D9, E be non empty set ; :: thesis: for d being Element of D
for d9 being Element of D9
for i being Nat
for F being Function of [:D,D9:],E holds F [:] (i |-> d),d9 = i |-> (F . d,d9)
let d be Element of D; :: thesis: for d9 being Element of D9
for i being Nat
for F being Function of [:D,D9:],E holds F [:] (i |-> d),d9 = i |-> (F . d,d9)
let d9 be Element of D9; :: thesis: for i being Nat
for F being Function of [:D,D9:],E holds F [:] (i |-> d),d9 = i |-> (F . d,d9)
let i be Nat; :: thesis: for F being Function of [:D,D9:],E holds F [:] (i |-> d),d9 = i |-> (F . d,d9)
let F be Function of [:D,D9:],E; :: thesis: F [:] (i |-> d),d9 = i |-> (F . d,d9)
thus F [:] (i |-> d),d9 = F .: (i |-> d),(i |-> d9) by FUNCOP_1:19
.= i |-> (F . d,d9) by Th18 ; :: thesis: verum