
theorem Th28: :: SPClique:
for R being RelStr, S being Subset of R, C being Clique of subrelstr S
 holds C is Clique of R
proof
 let R be RelStr, S be Subset of R, C be Clique of subrelstr S;
A1: the carrier of subrelstr S = S by YELLOW_0:def 15;
  now
   let a, b be Element of R such that
  A2: a in C and
  A3: b in C and
  A4: a <> b;
     reconsider a9 = a, b9 = b as Element of subrelstr S by A2,A3;
        a9 <= b9 or b9 <= a9 by A2,A3,A4,Th6;
   hence a <= b or b <= a by YELLOW_0:59;
  end;
 hence C is Clique of R by A1,Th6,XBOOLE_1:1;
end;
