When an ASBR in area 1 redistributes from another routing protocol into OSPF, that router generates type 5 LSAs through the area. When the ABRs of that area receive that type 5 lsas, they convert them to type 4. My question is: when that type 4 lsa gets flooded through area 0 and hits another ABR that is connected to area 2, what does THAT abr do with the type 4 lsa it received? Because now a router in area 2 isn't going to be able to look at the type 4 lsa and say the cost is "my cost to abr + the abr's cost to asbr" because it really would be "my cost to abr + the abr's cost to the next abr connected to area 1 + the abr's cost to the asbr".
My next question is with NSSA areas. When an ASBR in an NSSA area advertises it's type 7 LSAs and those LSAs are received by the ABR, the ABR will convert them to type 5 -- why wouldn't it convert them to type 4?