set L = ExWALattice ;
reconsider x = 1, y = 2, z = 3 as Element of ExWALattice by ENUMSET1:def 3;
reconsider xx = x, yy = y, zz = z as Element of {0,1,2,3,4} ;
yy ex1234"/\" zz =
min (yy,zz)
by ExMeetDef
.=
2
by XXREAL_0:def 9
;
then t1: x "/\" (y "/\" z) =
x "/\" y
by EXNDef
.=
xx ex1234"/\" yy
by EXNDef
.=
min (xx,yy)
by ExMeetDef
.=
1
by XXREAL_0:def 9
;
xx ex1234"/\" yy =
min (xx,yy)
by ExMeetDef
.=
1
by XXREAL_0:def 9
;
then (x "/\" y) "/\" z =
x "/\" z
by EXNDef
.=
xx ex1234"/\" zz
by EXNDef
.=
3
by ExMeetDef
;
hence
not ExWALattice is meet-associative
by LATTICES:def 7, t1; verum