
theorem
  for n being Nat, X being non empty set, f being Function of n
  -tuples_on X, X, p,q being FinSeqLen of n holds 1GateCircuit(p,f) tolerates
  1GateCircuit(q,f)
proof
  let n be Nat, X be non empty set, f be Function of n-tuples_on X, X;
  let p,q be FinSeqLen of n;
  set S1 = 1GateCircStr(p,f), S2 = 1GateCircStr(q,f);
  set A1 = 1GateCircuit(p,f), A2 = 1GateCircuit(q,f);
  thus 1GateCircStr(p,f) tolerates 1GateCircStr(q,f) by Th43;
A1: the Sorts of A2 = (the carrier of S2) --> X by Def13;
  the Sorts of A1 = (the carrier of S1) --> X by Def13;
  hence the Sorts of A1 tolerates the Sorts of A2 by A1,FUNCOP_1:87;
A2: the Charact of A2 = (q,f) .--> f by Th54;
  the Charact of A1 = (p,f) .--> f by Th54;
  hence thesis by A2,FUNCOP_1:87;
end;
