reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];
reserve a for Element of [:Fin X, Fin X:];
reserve A for set;
reserve x,y for Element of [:Fin X, Fin X:],
  a,b for Element of DISJOINT_PAIRS X;

theorem Th26:
  x c= b implies x is Element of DISJOINT_PAIRS X
proof
  assume
A1: x`1 c= b`1 & x`2 c= b`2;
  b`1 misses b`2 by Th23;
  then x`1 misses x`2 by A1,XBOOLE_1:64;
  hence thesis by Th23;
end;
