let X be non empty set ; :: thesis: for x1, x2 being Element of X st UnitBag x1 = UnitBag x2 holds
x1 = x2
let x1, x2 be Element of X; :: thesis: ( UnitBag x1 = UnitBag x2 implies x1 = x2 )
assume that
A1: UnitBag x1 = UnitBag x2 and
A2: x1 <> x2 ; :: thesis: contradiction
1 = (UnitBag x2) . x1 by A1, Th9
.= 0 by A2, Th9 ;
hence contradiction ; :: thesis: verum