
theorem Th54:
  for n being Nat, X being non empty set, f being Function of n
-tuples_on X, X for p being FinSeqLen of n holds the Charact of 1GateCircuit(p,
f) = (p,f) .--> f & for v being Vertex of 1GateCircStr(p,f) holds (the Sorts of
  1GateCircuit(p,f)).v = X
proof
  let n be Nat, X be non empty set, f be Function of n-tuples_on X, X;
  let p be FinSeqLen of n;
  set S = 1GateCircStr(p,f), A = 1GateCircuit(p,f);
  (the Charact of A).[p,f] = f by Def13;
  then
A1: for x being object st x in {[p,f]} holds (the Charact of A).x = f by
TARSKI:def 1;
  the carrier' of S = {[p,f]} by Def6;
  then dom the Charact of A = {[p,f]} by PARTFUN1:def 2;
  hence the Charact of A = (p,f) .--> f by A1,FUNCOP_1:11;
  let v be Vertex of S;
  the Sorts of A = (the carrier of S) --> X by Def13;
  hence thesis;
end;
