
theorem Th17:
  for A being non empty set, o being OperSymbol of CatSign A st o
  `1 = 1 or len o`2 = 1 ex a being Element of A st o = idsym(a)
proof
  let A be non empty set, o be OperSymbol of CatSign A such that
A1: o`1 = 1 or len o`2 = 1;
  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
A2: o`1 in {1} & o`2 in 1-tuples_on A & o = [o`1,o`2] or o`1 in {2} & o`2 in
  3-tuples_on A by MCART_1:10,21;
  then consider a being set such that
A3: a in A and
A4: o`2 = <*a*> by A1,CARD_1:def 7,FINSEQ_2:135,TARSKI:def 1;
  reconsider a as Element of A by A3;
  take a;
  thus thesis by A1,A2,A4,CARD_1:def 7,TARSKI:def 1;
end;
