
theorem Th16:
  for A being non empty set, o being OperSymbol of CatSign A holds
  o`1 = 1 & len o`2 = 1 or o`1 = 2 & len o`2 = 3
proof
  let A be non empty set, o be OperSymbol of CatSign A;
  the carrier' of CatSign A = [:{1},1-tuples_on A:] \/ [:{2},3-tuples_on A
  :] by Def3;
  then o in [:{1},1-tuples_on A:] or o in [:{2},3-tuples_on A:] by
XBOOLE_0:def 3;
  then o`1 in {1} & o`2 in 1-tuples_on A or o`1 in {2} & o`2 in 3-tuples_on A
  by MCART_1:10;
  hence thesis by CARD_1:def 7,TARSKI:def 1;
end;
