reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Subspace of V;
reserve x for set;
reserve w,w1,w2 for VECTOR of W;

theorem Th42:
  u in W & v in W implies u - v in W
proof
  assume
A1: u in W;
  assume v in W;
  then - v in W by Th41;
  hence thesis by A1,Th39;
end;
