reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem Th2:
  for i being Integer st (-3)/2 < i < 1/2 holds i = 0 or i = -1
  proof
    let i be Integer;
    assume
A1: (-3)/2 < i < 1/2;
    assume
A2: not (i=0 or i= -1);
    (-2) < i < 1 by A1,XXREAL_0:2;
    then
A3: (-2) + 1 <= i & i + 1 <= 1 & 0 <= 1 by INT_1:7;
    then
A4: (-1) <= i & i + 1 - 1 <= 1 - 1 by XREAL_1:9;
    consider k be Nat such that
A5: i = k or i = - k by INT_1:2;
    per cases by A5;
    suppose i = k;
      hence contradiction by A2,A4;
    end;
    suppose
A6:   i = - k;
      then (-k) * (-1) <= (-1) * (-1) by A3,XREAL_1:65;
      then k = 0 or ... or k = 1;
      hence contradiction by A6,A2;
    end;
  end;
