
theorem
  for f,x being set, p being FinSequence for g being Gate of
1GateCircStr(p,f,x) holds g = [p,f] & the_arity_of g = p & the_result_sort_of g
  = x
proof
  let f,x be set, p be FinSequence;
  set S = 1GateCircStr(p,f,x);
  let o be Gate of 1GateCircStr(p,f,x);
A1: (the ResultSort of S).[p,f] = x by Def5;
A2: the carrier' of S = {[p,f]} by Def5;
  hence o = [p,f] by TARSKI:def 1;
  (the Arity of S).[p,f] = p by Def5;
  hence thesis by A2,A1,TARSKI:def 1;
end;
