let D be non empty set ; for d1, d2 being Element of D
for i being natural Number
for T being Tuple of i,D
for F, G being BinOp of D st F is_distributive_wrt G holds
F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T)))
let d1, d2 be Element of D; for i being natural Number
for T being Tuple of i,D
for F, G being BinOp of D st F is_distributive_wrt G holds
F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T)))
let i be natural Number ; for T being Tuple of i,D
for F, G being BinOp of D st F is_distributive_wrt G holds
F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T)))
let T be Tuple of i,D; for F, G being BinOp of D st F is_distributive_wrt G holds
F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T)))
let F, G be BinOp of D; ( F is_distributive_wrt G implies F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T))) )
assume A1:
F is_distributive_wrt G
; F [;] ((G . (d1,d2)),T) = G .: ((F [;] (d1,T)),(F [;] (d2,T)))