let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF

for u, v being Element of V

for W being Subspace of V st u in W & v in W holds

u - v in W

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for u, v being Element of V

for W being Subspace of V st u in W & v in W holds

u - v in W

let u, v be Element of V; :: thesis: for W being Subspace of V st u in W & v in W holds

u - v in W

let W be Subspace of V; :: thesis: ( u in W & v in W implies u - v in W )

assume that

A1: u in W and

A2: v in W ; :: thesis: u - v in W

- v in W by A2, Th22;

hence u - v in W by A1, Th20; :: thesis: verum

for u, v being Element of V

for W being Subspace of V st u in W & v in W holds

u - v in W

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for u, v being Element of V

for W being Subspace of V st u in W & v in W holds

u - v in W

let u, v be Element of V; :: thesis: for W being Subspace of V st u in W & v in W holds

u - v in W

let W be Subspace of V; :: thesis: ( u in W & v in W implies u - v in W )

assume that

A1: u in W and

A2: v in W ; :: thesis: u - v in W

- v in W by A2, Th22;

hence u - v in W by A1, Th20; :: thesis: verum