let D be non empty set ; :: thesis: for F being BinOp of D
for u being UnOp of D
for p being FinSequence of D st F is having_a_unity & u . (the_unity_wrt F) = the_unity_wrt F & u is_distributive_wrt F holds
u . (F "**" p) = F "**" (u * p)
let F be BinOp of D; :: thesis: for u being UnOp of D
for p being FinSequence of D st F is having_a_unity & u . (the_unity_wrt F) = the_unity_wrt F & u is_distributive_wrt F holds
u . (F "**" p) = F "**" (u * p)
let u be UnOp of D; :: thesis: for p being FinSequence of D st F is having_a_unity & u . (the_unity_wrt F) = the_unity_wrt F & u is_distributive_wrt F holds
u . (F "**" p) = F "**" (u * p)
let p be FinSequence of D; :: thesis: ( F is having_a_unity & u . (the_unity_wrt F) = the_unity_wrt F & u is_distributive_wrt F implies u . (F "**" p) = F "**" (u * p) )
assume A1: ( F is having_a_unity & u . (the_unity_wrt F) = the_unity_wrt F ) ; :: thesis: ( not u is_distributive_wrt F or u . (F "**" p) = F "**" (u * p) )
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 "**" p) = F "**" (u * p)
hence u . (F "**" p) = F "**" (u * p) by A1, Th39; :: thesis: verum