
theorem Th46:
  for f being object, p being FinSequence holds 1GateCircStr(p,f) is
  unsplit gate`1=arity
proof
  let f be object, p be FinSequence;
  set S = 1GateCircStr(p,f);
A1: now
    let x be object;
    assume x in {[p,f]};
    then x = [p,f] by TARSKI:def 1;
    hence (the ResultSort of S).x = x by Def6;
  end;
A2: the carrier' of S = {[p,f]} by Def6;
  then dom the ResultSort of S = {[p,f]} by FUNCT_2:def 1;
  hence the ResultSort of S = id the carrier' of S by A2,A1,FUNCT_1:17;
  let g be set;
  assume g in the carrier' of S;
  then
A3: g = [p,f] by A2,TARSKI:def 1;
  then (the Arity of S).g = p by Def6;
  hence thesis by A3;
end;
