parad0xica
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What aboutThat doesn't look correct. The corollary of the triangle inequality does not state |a-b| < |a|-|b|
the closest I know of is ||x|-|y||<|x-y|
But that contradicts what you suppose.
|x + y| < |x| + |y|
Let y = -y,
|x - y| < |x| + |-y| = |x| + |y|?