With and two vectors, the triangle inequality can be written as:
which can be broken down into a system of inequalities (labelled as (1) and (2)):
then, with the assumption of , (1)-(2) yields:
But is this in fact true? Is (B) a direct consequence of (A) when ? or is (B) is invalid because (1)-(2) is not allowed as it is not obvious if the subtraction preserves the inequality?