let V be RealUnitarySpace; :: thesis: for W being Subspace of V
for u, v being VECTOR of V holds
( v - u in v + W iff u in W )
let W be Subspace of V; :: thesis: for u, v being VECTOR of V holds
( v - u in v + W iff u in W )
let u, v be VECTOR 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 Th16;
( u in W implies - u in W ) by Th16;
hence ( v - u in v + W iff u in W ) by A1, A2, Th55, RLVECT_1:17; :: thesis: verum