let a, b be Element of ExWALattice; :: thesis: ( b = 0 implies a "\/" b = a )
reconsider aa = a, bb = b as Element of {0,1,2,3,4} ;
A0: 0 <= aa by ENUMSET1:def 3;
assume A1: b = 0 ; :: thesis: a "\/" b = a
a "\/" b = aa ex1234"\/" bb by EXUDef
.= max (aa,0) by A1, UPDef
.= aa by A0, XXREAL_0:def 10 ;
hence a "\/" b = a ; :: thesis: verum