can a monster destroy by effect after it was destroyed by battle?

when the attacking monster inflict battle damage by attacking opponent monster,the attack target is consider as destroy by battle at that moment.

so,can a monster destry by effect after that? yes,this could be happen.this prove by following example :

1) red demon dragon-
when red demon dragon attack def position monster,include the attack target monster also consider as destroy by effect after damage calculation~(giant rat can't active their effect~)

2)when negate the monster effect :
those flip monster or DD lady ,they destroy by effect after you negate their effect~

3)rivalry of warlords-
if the set monster type is diffence with your face up monster,it sent to graveyard after damage calculation~