I have an Ali from Cairo in play and I am at one life. My opponent has a tarmgoyf and has just equipped Sword of fire and ice and swings for 6.
Arabian Nights
Card Type: Creature
Creature Type: Human
Power/Toughness: 0/1
Casting Cost: 2RR
Card Text: While Ali is in play, damage that would reduce you to less than 1 life lowers you to 1 life. All further damage is prevented.
Oracle Text: Damage that would reduce your life total to less than 1 reduces it to 1 instead.
Notice the original card text/oracle text is different and perhaps functionally different. Does tarmgoyf hit me for 6, reduced to 0, allowing my opponent to draw a card and shoot off Ali? Or does tarm's damage become "prevented" and thus my Ali continues to live?
The oracle text simply changes the result of damage being dealt to you (life loss is the normal result, but damage dealt by infect sources for instance yields a different result), it does not prevent nor reduce the damage. So sword triggers.