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