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 [;] d,T' = (F [;] d,(id 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 [;] d,T' = (F [;] d,(id 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 [;] d,T' = (F [;] d,(id D')) * T'
let F be Function of [:D,D':],E; :: thesis: for T' being Element of i -tuples_on D' holds F [;] d,T' = (F [;] d,(id D')) * T'
let T' be Element of i -tuples_on D'; :: thesis: F [;] d,T' = (F [;] d,(id D')) * T'
rng T' c= D' by FINSEQ_1:def 4;
hence F [;] d,T' = F [;] d,((id D') * T') by RELAT_1:79
.= (F [;] d,(id D')) * T' by FUNCOP_1:44 ;
:: thesis: verum