reserve V for RealLinearSpace;
reserve p,q,u,v,w,y for VECTOR of V;
reserve a,b,c,d for Real;

theorem Th5:
  a<>0 & a*u=v implies u=a"*v
proof
  assume that
A1: a<>0 and
A2: a*u=v;
  thus u=1*u by RLVECT_1:def 8
    .=(a"*a)*u by A1,XCMPLX_0:def 7
    .=a"*v by A2,RLVECT_1:def 7;
end;
