set O = the non trivial 1-sorted ;
reconsider tau = {} as Subset-Family of the non trivial 1-sorted by XBOOLE_1:2;
take TopStruct(# the carrier of the non trivial 1-sorted ,tau #) ; :: thesis: ( not TopStruct(# the carrier of the non trivial 1-sorted ,tau #) is trivial & TopStruct(# the carrier of the non trivial 1-sorted ,tau #) is strict )
thus ( not TopStruct(# the carrier of the non trivial 1-sorted ,tau #) is trivial & TopStruct(# the carrier of the non trivial 1-sorted ,tau #) is strict ) ; :: thesis: verum