reserve i,j,k,n for Nat;
reserve x,x1,x2,x3,y1,y2,y3 for set;

theorem
  for i,j,n be Nat holds i < j & j in Segm n implies i in Segm n
proof
  let i,j,n be Nat;
  assume that
A1: i < j and
A2: j in Segm n;
  j < n by A2,NAT_1:44;
  then i < n by A1,XXREAL_0:2;
  hence thesis by NAT_1:44;
end;
