let Y be non empty TopStruct ; :: thesis: for A being non empty Subset of Y holds TopStruct(# the carrier of (MaxADSspace A),the topology of (MaxADSspace A) #) = TopStruct(# the carrier of (MaxADSspace (MaxADSet A)),the topology of (MaxADSspace (MaxADSet A)) #)
let A be non empty Subset of Y; :: thesis: TopStruct(# the carrier of (MaxADSspace A),the topology of (MaxADSspace A) #) = TopStruct(# the carrier of (MaxADSspace (MaxADSet A)),the topology of (MaxADSspace (MaxADSet A)) #)
( the carrier of (MaxADSspace A) = MaxADSet A & the carrier of (MaxADSspace (MaxADSet A)) = MaxADSet (MaxADSet A) ) by Def19;
hence TopStruct(# the carrier of (MaxADSspace A),the topology of (MaxADSspace A) #) = TopStruct(# the carrier of (MaxADSspace (MaxADSet A)),the topology of (MaxADSspace (MaxADSet A)) #) by Th35, TSEP_1:5; :: thesis: verum