let Y be non empty TopStruct ; :: thesis: for x, y being Point of Y holds
( the carrier of (MaxADSspace x) misses the carrier of (MaxADSspace y) or TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace y),the topology of (MaxADSspace y) #) )
let x, y be Point of Y; :: thesis: ( the carrier of (MaxADSspace x) misses the carrier of (MaxADSspace y) or TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace y),the topology of (MaxADSspace y) #) )
A1: ( the carrier of (MaxADSspace x) = MaxADSet x & the carrier of (MaxADSspace y) = MaxADSet y ) by Def17;
assume the carrier of (MaxADSspace x) meets the carrier of (MaxADSspace y) ; :: thesis: TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace y),the topology of (MaxADSspace y) #)
hence TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace y),the topology of (MaxADSspace y) #) by A1, Th24, TSEP_1:5; :: thesis: verum