take S = 2-sorted(# {},{} #); :: thesis: ( S is strict & S is empty & S is void )

thus S is strict ; :: thesis: ( S is empty & S is void )

thus the carrier of S is empty ; :: according to STRUCT_0:def 1 :: thesis: S is void

thus the carrier' of S is empty ; :: according to STRUCT_0:def 13 :: thesis: verum

thus S is strict ; :: thesis: ( S is empty & S is void )

thus the carrier of S is empty ; :: according to STRUCT_0:def 1 :: thesis: S is void

thus the carrier' of S is empty ; :: according to STRUCT_0:def 13 :: thesis: verum