User blog comment:Vel!/1+w/@comment-5982810-20141011205302/@comment-1605058-20141011210041

"If a<b then w^a+w^b=w^b" is simple property of ordinals: by left distributivity of multiplication, we get that w^a+w^b=w^a(1+w^(b-a))=w^a*w^(b-a)=w^(a+(b-a))=w^b, where b-a is the least ordinal c such that a+c=b.