
theorem Th19: :: Height4:
for R being with_finite_clique# RelStr st clique# R = 1
  holds [#]R is StableSet of R
proof
 let R be with_finite_clique# RelStr;
 assume A1: clique# R = 1;
 set cR = the carrier of R;
A2: R is non empty by A1;
 now
   let a, b be Element of R such that
    a in cR and b in cR and
 A3: a <> b;
   assume a <= b or b <= a;
   then A4: {a,b} is Clique of R by A2,Th8;
    card {a,b} = 2 by A3,CARD_2:57;
   hence contradiction by A4,A1,Def4;
 end;
 hence [#]R is StableSet of R by Def2;
end;
