
theorem Th15: :: ACClique:
for R being RelStr, C being Clique of R, A being StableSet of R, a, b being set
 st a in A & b in A & a in C & b in C holds a = b
proof
 let R be RelStr, C be Clique of R, A be StableSet of R, a, b be set such that
A1: a in A & b in A and
A2: a in C & b in C;
  assume A3: a <> b;
   reconsider a9 = a, b9 = b as Element of R by A1;
   not a9 <= b9 & not b9 <= a9 by A1,A3,Def2;
  hence contradiction by A2,A3,Th6;
end;
