theorem Th10: :: PAPDESAF:10

for V being RealLinearSpace
for o, u, v, u1, v1 being VECTOR of V
for r being Real st o - u = r * (u1 - o) & r <> 0 & o,v '||' o,v1 & not o,u '||' o,v & u,v '||' u1,v1 holds
( v1 = u1 + (((- r) ") * (v - u)) & v1 = o + (((- r) ") * (v - o)) & v - u = (- r) * (v1 - u1) )