theorem Th1:
  for x,y being Nat st x < y < x+2 holds y = x+1
  proof
    let x,y be Nat;
    assume x < y;
    then
A1: x+1 <= y by NAT_1:13;
    assume y < x+2;
    then y < x+1+1;
    then y <= x+1 by NAT_1:13;
    hence y = x+1 by A1,XXREAL_0:1;
  end;
