reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;

theorem Th7:
  u,v are_Ort_wrt w,y implies a*u,v are_Ort_wrt w,y & u,b*v are_Ort_wrt w,y
proof
A1: v = 1*v & u = 1*u by RLVECT_1:def 8;
  assume u,v are_Ort_wrt w,y;
  hence thesis by A1,Th6;
end;
