reserve r,lambda for Real,
  i,j,n for Nat;
reserve p,p1,p2,q1,q2 for Point of TOP-REAL 2,
  P, P1 for Subset of TOP-REAL 2;
reserve T for TopSpace;

theorem
  R^2-unit_square ={ p : p`1 = 0 & p`2 <= 1 & p`2 >= 0 or p`1 <= 1 & p`1
>= 0 & p`2 = 1 or p`1 <= 1 & p`1 >= 0 & p`2 = 0 or p`1 = 1 & p`2 <= 1 & p`2 >=
  0}
proof
  defpred X4[Point of TOP-REAL 2] means $1`1 = 1 & $1`2 <= 1 & $1`2 >= 0;
  defpred X3[Point of TOP-REAL 2] means $1`1 <= 1 & $1`1 >= 0 & $1`2 = 0;
  defpred X2[Point of TOP-REAL 2] means $1`1 <= 1 & $1`1 >= 0 & $1`2 = 1;
  defpred X1[Point of TOP-REAL 2] means $1`1 = 0 & $1`2 <= 1 & $1`2 >= 0;
  defpred X34[Point of TOP-REAL 2] means $1`1 <= 1 & $1`1 >= 0 & $1`2 = 0 or
  $1`1 = 1 & $1`2 <= 1 & $1`2 >= 0;
  defpred X12[Point of TOP-REAL 2] means $1`1 = 0 & $1`2 <= 1 & $1`2 >= 0 or
  $1`1 <= 1 & $1`1 >= 0 & $1`2 = 1;
  set L1 = { p : X1[p]}, L2 = { p : X2[p]}, L3 = { p : X3[p]}, L4 = { p : X4[p
  ]};
A1: { p2 : X12[p2] or X34[p2] } = { p : X12[p] } \/ { q1: X34[q1] } from
  FraenkelAlt;
A2: { q1: X3[q1] or X4[q1] } = L3 \/ L4 from FraenkelAlt
    .= LSeg(|[ 0,0 ]|, |[ 1,0 ]|) \/ LSeg(|[ 1,0 ]|, |[ 1,1 ]|) by Th13;
  { p : X1[p] or X2[p] } = L1 \/ L2 from FraenkelAlt
    .= LSeg(|[0,0]|,|[0,1]|) \/ LSeg(|[ 0,1 ]|, |[ 1,1 ]|) by Th13;
  hence thesis by A1,A2;
end;
