let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF
for v, u being Element of V
for W being Subspace of V holds
( v - u in v + W iff u in W )
let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for v, u being Element of V
for W being Subspace of V holds
( v - u in v + W iff u in W )
let v, u be Element of V; :: thesis: for W being Subspace of V holds
( v - u in v + W iff u in W )
let W be Subspace of V; :: thesis: ( v - u in v + W iff u in W )
A1: v - u = (- u) + v ;
A2: ( - u in W implies - (- u) in W ) by Th30;
( u in W implies - u in W ) by Th30;
hence ( v - u in v + W iff u in W ) by A1, A2, Th75, RLVECT_1:17; :: thesis: verum