Question on wording(Yes this is for a set)

[Piercer of the Heavens]

If a card effect requires you to[u] PAY[/u] life points would you be able to Special Summon a monster who's effect is: "When you take damage(either by battle or by card effect) you can Special Summon this card from your hand or graveyard. " or would I need to change the effect to "When your life points decrease you can Special Summon this card from you hand or graveyard."

[Flash Flyer - Sakura]

I think you'd have to change it to "if your Life Points decrease..."

[Piercer of the Heavens]

I was thinking that to, but I just wanted to make sure. So thank you.