let Y, X be non empty set ; :: thesis: for F being BinOp of X
for f being Function of Y,X
for g being Function of X,X holds (F .: (id X),g) * f = F .: f,(g * f)
let F be BinOp of X; :: thesis: for f being Function of Y,X
for g being Function of X,X holds (F .: (id X),g) * f = F .: f,(g * f)
let f be Function of Y,X; :: thesis: for g being Function of X,X holds (F .: (id X),g) * f = F .: f,(g * f)
let g be Function of X,X; :: thesis: (F .: (id X),g) * f = F .: f,(g * f)
thus (F .: (id X),g) * f = F .: ((id X) * f),(g * f) by Th31
.= F .: f,(g * f) by FUNCT_2:23 ; :: thesis: verum