let C, D be non empty set ; :: thesis: for f, f' being Function of C,D
for F being BinOp of D
for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: f,f') = F .: (u * f),(u * f')
let f, f' be Function of C,D; :: thesis: for F being BinOp of D
for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: f,f') = F .: (u * f),(u * f')
let F be BinOp of D; :: thesis: for u being UnOp of D st u is_distributive_wrt F holds
u * (F .: f,f') = F .: (u * f),(u * f')
let u be UnOp of D; :: thesis: ( u is_distributive_wrt F implies u * (F .: f,f') = F .: (u * f),(u * f') )
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 .: f,f') = F .: (u * f),(u * f')
hence u * (F .: f,f') = F .: (u * f),(u * f') by Th38; :: thesis: verum