
theorem Th36:
  for f,x being set, p being FinSequence holds the Arity of
1GateCircStr(p,f,x) = (p,f) .--> p & the ResultSort of 1GateCircStr(p,f,x) = (p
  ,f) .--> x
proof
  let f,x be set, p be FinSequence;
  set S = 1GateCircStr(p,f,x);
  (the Arity of S).[p,f] = p by Def5;
  then
A1: for x being object st x in {[p,f]} holds (the Arity of S).x = p by
TARSKI:def 1;
A2: the carrier' of S = {[p,f]} by Def5;
  then dom the Arity of S = {[p,f]} by FUNCT_2:def 1;
  hence the Arity of S = (p,f) .--> p by A1,FUNCOP_1:11;
  (the ResultSort of S).[p,f] = x by Def5;
  then
A3: for y being object st y in {[p,f]} holds (the ResultSort of S).y = x by
TARSKI:def 1;
  dom the ResultSort of S = {[p,f]} by A2,FUNCT_2:def 1;
  hence thesis by A3,FUNCOP_1:11;
end;
