let K be non empty doubleLoopStr ; for V, W being non empty ModuleStr over K
for f being Form of V,W
for a being Element of K
for v being Vector of V holds FunctionalFAF ((a * f),v) = a * (FunctionalFAF (f,v))
let V, W be non empty ModuleStr over K; for f being Form of V,W
for a being Element of K
for v being Vector of V holds FunctionalFAF ((a * f),v) = a * (FunctionalFAF (f,v))
let f be Form of V,W; for a being Element of K
for v being Vector of V holds FunctionalFAF ((a * f),v) = a * (FunctionalFAF (f,v))
let a be Element of K; for v being Vector of V holds FunctionalFAF ((a * f),v) = a * (FunctionalFAF (f,v))
let w be Vector of V; FunctionalFAF ((a * f),w) = a * (FunctionalFAF (f,w))
hence
FunctionalFAF ((a * f),w) = a * (FunctionalFAF (f,w))
by FUNCT_2:63; verum