
theorem Th25:
  for S1,S2,S3 be unsplit gate`1=arity gate`2isBoolean non void
  non empty ManySortedSign for A1 being Boolean Circuit of S1, A2 being Boolean
Circuit of S2 for A3 being Boolean Circuit of S3 holds (A1+*A2)+*A3 = A1+*(A2+*
  A3)
proof
  let S1,S2,S3 be unsplit gate`1=arity gate`2isBoolean non void non empty
  ManySortedSign;
  let A1 be Boolean Circuit of S1;
  let A2 be Boolean Circuit of S2;
  let A3 be Boolean Circuit of S3;
A1: the Sorts of A3 tolerates the Sorts of A1 by CIRCCOMB:59;
  the Sorts of A1 tolerates the Sorts of A2 & the Sorts of A2 tolerates
  the Sorts of A3 by CIRCCOMB:59;
  hence thesis by A1,CIRCCOMB:23;
end;
