
theorem Th1:
  for X being finite non empty set, n being Nat for p being
FinSeqLen of n for f being Function of n-tuples_on X, X for o being OperSymbol
  of 1GateCircStr(p,f) for s being State of 1GateCircuit(p,f) holds o
  depends_on_in s = s*p
proof
  let X be finite non empty set;
  let n be Nat;
  let p be FinSeqLen of n;
  let f be Function of n-tuples_on X, X;
  let o be OperSymbol of 1GateCircStr(p,f);
  let s be State of 1GateCircuit(p,f);
  o depends_on_in s = s * (the_arity_of o) by CIRCUIT1:def 3
    .= s*p by CIRCCOMB:41;
  hence thesis;
end;
