let V be RealUnitarySpace; :: thesis: for W being Subspace of V
for u, v being VECTOR of V st u in W & v in W holds
u - v in W
let W be Subspace of V; :: thesis: for u, v being VECTOR of V st u in W & v in W holds
u - v in W
let u, v be VECTOR 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, Th16;
hence u - v in W by A1, Th14; :: thesis: verum