BS13-061 The Coronation Volcano VS BS13-066 The Great Tree of Life

does the effect of "The Coronation Volcano" on opponent side of field, activate my effect of "The Great Tree of Life",
so i can get cores??

BS13-061] MT. CORONA, THE FLAME-CROWNED VOLCANO {3} -1R
The Coronation Volcano (戴冠する活火山 Taikan-suru Kakkazan)
Common Ruby Nexus [R]
Level 1 <0>, Level 2 <1>
{Featured Constellation: Corona Australis, "the Southern Crown"}

During Each Attack Phase (Lv. 1-2): When a Spirit with 4000BP or less attacks, that Spirit is destroyed.

--

[BS13-066] GREAT TREE OF LIFE {4} -3E
The Great Tree of Life (生命司る大樹 Inochi Tsukasadoru Daiju)
Common Emerald Nexus [E]
Level 1 <0>, Level 2 <2>

(Lv. 1-2): When your opponent destroys one of your Spirits, add a Core from the Void to your Reserve.

Yes, effects of The Great Tree of Life applies when your spirits is destroyed by opponent's effects, attacks or blocks. Another example is when the opponent uses Deadly Balance.

thnx for qucíck help:-)