let GF be non empty right_complementable associative commutative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for a, b being Element of
for v being Element of holds (a - b) * v = (a * v) - (b * v)
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for a, b being Element of
for v being Element of holds (a - b) * v = (a * v) - (b * v)
let a, b be Element of ; :: thesis: for v being Element of holds (a - b) * v = (a * v) - (b * v)
let v be Element of ; :: thesis: (a - b) * v = (a * v) - (b * v)
thus (a - b) * v = (a * v) + ((- b) * v) by VECTSP_1:def 26
.= (a * v) - (b * v) by VECTSP_1:68 ; :: thesis: verum