Why did Edom make a point of mentioning 'the sword'?
Rashi: In response to Yisrael's request, 1 he replied that just as Yisrael proudly referred to their inheritance of "ha'Kol Kol Ya'akov!", he was now putting into practice his inheritance of "ve'al Charb'cha Yichyeh!" with which he was now coming to meet them. 2
Seforno: What the king actually meant was
Seeing as Moshe addressed the king of Edom, why does the Torah refer to 'Edom'?
Ramban: Because the people seconded the king's refusal to allow Yisrael passage via their land.