let V be ComplexLinearSpace; :: thesis: for u, v being VECTOR of V
for W being Subspace of V st u in W & v in W holds
u - v in W
let u, v be VECTOR 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 A1: u in W ; :: thesis: ( not v in W or u - v in W )
assume v in W ; :: thesis: u - v in W
then - v in W by Th41;
hence u - v in W by A1, Th39; :: thesis: verum