let X be Tolerance_Space; :: thesis: for a, b, c being Element of (RSLattice X) holds a "/\" (b "/\" c) = (a "/\" b) "/\" c
let a, b, c be Element of (RSLattice X); :: thesis: a "/\" (b "/\" c) = (a "/\" b) "/\" c
reconsider a1 = a, b1 = b, c1 = c as Element of RoughSets X by Def8;
reconsider a9 = a1, b9 = b1, c9 = c1 as RoughSet of X by DefRSX;
set G = RSLattice X;
XX: b9 _/\_ c9 is Element of RoughSets X by DefRSX;
XY: a9 _/\_ b9 is Element of RoughSets X by DefRSX;
a "/\" (b "/\" c) = the L_meet of (RSLattice X) . a1,(b9 _/\_ c9) by Def8
.= a9 _/\_ (b9 _/\_ c9) by Def8, XX
.= (a9 _/\_ b9) _/\_ c9 by Th8
.= the L_meet of (RSLattice X) . (a9 _/\_ b9),c1 by Def8, XY
.= (a "/\" b) "/\" c by Def8 ;
hence a "/\" (b "/\" c) = (a "/\" b) "/\" c ; :: thesis: verum