let D be non empty set ; :: thesis: for i being Nat
for T1, T2 being Element of i -tuples_on D
for F being BinOp of D
for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: T1,T2) = F .: (u * T1),(u * T2)
let i be Nat; :: thesis: for T1, T2 being Element of i -tuples_on D
for F being BinOp of D
for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: T1,T2) = F .: (u * T1),(u * T2)
let T1, T2 be Element of i -tuples_on D; :: thesis: for F being BinOp of D
for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: T1,T2) = F .: (u * T1),(u * T2)
let F be BinOp of D; :: thesis: for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: T1,T2) = F .: (u * T1),(u * T2)
let u be UnOp of D; :: thesis: ( u is_distributive_wrt F implies u * (F .: T1,T2) = F .: (u * T1),(u * T2) )
assume for d1, d2 being Element of D holds u . (F . d1,d2) = F . (u . d1),(u . d2) ; :: according to BINOP_1:def 20 :: thesis: u * (F .: T1,T2) = F .: (u * T1),(u * T2)
hence u * (F .: T1,T2) = F .: (u * T1),(u * T2) by Th49; :: thesis: verum