
theorem
  for f,x being set, p being FinSequence holds 1GateCircStr(p,f,x) is
  gate`1=arity Circuit-like
proof
  let f,x be set;
  let p be FinSequence;
  set S = 1GateCircStr(p,f,x);
  thus S is gate`1=arity
  proof
    let g be set;
    assume g in the carrier' of S;
    then g in {[p,f]} by CIRCCOMB:def 5;
    then
A1: g = [p,f] by TARSKI:def 1;
    thus thesis by A1,CIRCCOMB:def 5;
  end;
  thus S is Circuit-like
  proof
    let S9 be non void non empty ManySortedSign such that
A2: S9 = S;
    let o1, o2 be OperSymbol of S9;
    o1 = [p,f] by A2,CIRCCOMB:37;
    hence thesis by A2,CIRCCOMB:37;
  end;
end;
