let Y be non empty set ; :: thesis: for PA, PB being a_partition of Y st ERl PA = ERl PB holds
PA = PB
let PA, PB be a_partition of Y; :: thesis: ( ERl PA = ERl PB implies PA = PB )
assume ERl PA = ERl PB ; :: thesis: PA = PB
then ( PA '<' PB & PB '<' PA ) by Th20;
hence PA = PB by Th4; :: thesis: verum