
theorem Th20: :: Width3:
for R being with_finite_stability# non empty RelStr
 st [#]R is Clique of R holds stability# R = 1
proof
 let R be with_finite_stability# non empty RelStr;
 assume A1: [#]R is Clique of R;
   A2: stability# R >= 0+1 by NAT_1:13;
   consider A being finite StableSet of R such that
 A3: card(A) = stability# R by Def6;
 assume stability# R <> 1;
 then card A > 1 by A2,A3,XXREAL_0:1;
 then consider a, b being set such that
 A4: a in A and
 A5: b in A and
 A6: a <> b by NAT_1:59;
 thus thesis by A4,A5,A6,A1,Th15;
end;
