Lux Ultimate no cooldown?

Lux R on PBE Rank 16 gives 50% Reduced cooldown on kill. The presence of mind rune buff on PBE grants 10% Reduced CD on ultimate if she kills someone with her ultimate, Ultimate hat gives 15% CDR if you use it 5 times and if you build 40% CDR you have a little bit over 100% CDR Do these cooldown stack ontop if each other or am I missing something?
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