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#y=u#w implies y=w
proof
  assume
A1: u#y=u#w;
  set p=u#y;
  u+y = p+p by Def2
    .= u+w by A1,Def2;
  hence thesis by RLVECT_1:8;
end;
