reserve V for RealLinearSpace,
  u,u1,u2,v,v1,v2,w,w1,x,y for VECTOR of V,
  a,a1,a2,b,b1,b2,c1,c2,n,k1,k2 for Real;

theorem Th12:
  Gen x,y implies Orte(x,y,n*u)=n*Orte(x,y,u)
proof
  assume
A1: Gen x,y;
  hence Orte(x,y,n*u)=n*pr2(x,y,u)*x + (-pr1(x,y,n*u))*y by Lm7
    .=n*pr2(x,y,u)*x + (-(n*pr1(x,y,u)))*y by A1,Lm7
    .=n*pr2(x,y,u)*x + (n*pr1(x,y,u))*(-y) by RLVECT_1:24
    .=n*pr2(x,y,u)*x + (-(n*pr1(x,y,u)*y)) by RLVECT_1:25
    .=n*pr2(x,y,u)*x + (-(n*(pr1(x,y,u)*y))) by RLVECT_1:def 7
    .=n*pr2(x,y,u)*x + n*(-(pr1(x,y,u)*y)) by RLVECT_1:25
    .=n*(pr2(x,y,u)*x) + n*(-(pr1(x,y,u)*y)) by RLVECT_1:def 7
    .=n*(pr2(x,y,u)*x + (-(pr1(x,y,u)*y))) by RLVECT_1:def 5
    .=n*(pr2(x,y,u)*x + (pr1(x,y,u)*(-y))) by RLVECT_1:25
    .=n*Orte(x,y,u) by RLVECT_1:24;
end;
