let Y be non empty TopStruct ; :: thesis: for x being Point of Y holds TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace {x}),the topology of (MaxADSspace {x}) #)
let x be Point of Y; :: thesis: TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace {x}),the topology of (MaxADSspace {x}) #)
A1: the carrier of (MaxADSspace {x}) = MaxADSet {x} by Def18;
the carrier of (MaxADSspace x) = MaxADSet x by Def17;
hence TopStruct(# the carrier of (MaxADSspace x),the topology of (MaxADSspace x) #) = TopStruct(# the carrier of (MaxADSspace {x}),the topology of (MaxADSspace {x}) #) by A1, Th30, TSEP_1:5; :: thesis: verum