
theorem Th21: :: Width4:
for R being with_finite_stability# RelStr st stability# R = 1
 holds [#]R is Clique of R
proof
 let R be with_finite_stability# RelStr;
 assume A1: stability# R = 1;
 set cR = the carrier of R;
 now
   let a, b be Element of R such that
 A2: a in cR and b in cR and
 A3: a <> b;
 A4: R is non empty by A2;
   assume not (a <= b or b <= a);
   then A5: {a,b} is StableSet of R by A4,Th14;
   card {a,b} = 2 by A3,CARD_2:57;
   hence contradiction by A1,Def6,A5;
 end;
 hence [#]R is Clique of R by Th6;
end;
