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 Th7:
  Gen x,y implies Ortm(x,y,Ortm(x,y,u))=u
proof
  assume
A1: Gen x,y;
  hence Ortm(x,y,Ortm(x,y,u))=
  pr1(x,y,u)*x+(-pr2(x,y,pr1(x,y,u)*x+(-pr2(x,y,u))*y))*y by GEOMTRAP:def 4
    .=pr1(x,y,u)*x+(-(-pr2(x,y,u)))*y by A1,GEOMTRAP:def 5
    .=u by A1,Lm5;
end;
