let T be sup-Semilattice; :: thesis: ( T is Noetherian implies T is Mizar-widening-like )
assume A1: T is Noetherian ; :: thesis: T is Mizar-widening-like
thus T is sup-Semilattice ; :: according to ABCMIZ_0:def 3 :: thesis: T is Noetherian
thus T is Noetherian by A1; :: thesis: verum