theorem Th36:
  arity (n proj i) = n
proof
  consider d being object such that
A1: d in n-tuples_on NAT by XBOOLE_0:def 1;
  reconsider d as Element of n-tuples_on NAT by A1;
A2: dom (n proj i) = n-tuples_on NAT by Th35;
  then
A3: for x be FinSequence st x in dom (n proj i) holds n= len x by CARD_1:def 7;
  d in dom (n proj i) by A2;
  hence thesis by A3,MARGREL1:def 25;
end;
