reserve x,y for object, X for set;

theorem Th18:
  for n be Nat st 1 < n holds card Segm0(n) = n-1
proof
  let n be Nat;
A1: card (Segm(n)) = n;
  assume
A2: 1 < n;
  then
A3: 0 in Segm(n) by NAT_1:44;
A4: card {0} = 1 by CARD_1:30;
  Segm0(n) = Segm(n) \{0} by A2,Def2;
  hence thesis by A1,A3,A4,EULER_1:4;
end;
