
theorem Th71: :: Width4:
for G being with_finite_stability# SimpleGraph
  st stability# G = 1 holds G is clique
proof
 let R be with_finite_stability# SimpleGraph;
 assume A1: stability# R = 1;
 set cR = Vertices R;
 now
   let a, b be set such that
 A2: a <> b and
 A3: a in cR & b in cR;
   assume {a, b} nin Edges R;
   then {a,b} nin R by A2,Th12;
   then A4: {a,b} is StableSet of R by A3,Th62;
   card {a,b} = 2 by A2,CARD_2:57;
   hence contradiction by A1,A4,Def24;
 end;
 hence R is clique by Th47;
end;
