reserve i,j,k,n,m for Nat;
reserve p,q for Point of TOP-REAL 2;
reserve G for Go-board;

theorem
  1 <= j & j <= k & k <= width G & 1 <= i & i <= len G implies G*(i,j)`2
  <= G*(i,k)`2
proof
  assume that
A1: 1 <= j and
A2: j <= k and
A3: k <= width G and
A4: 1 <= i and
A5: i <= len G;
  per cases by A2,XXREAL_0:1;
  suppose
    j < k;
    hence thesis by A1,A3,A4,A5,GOBOARD5:4;
  end;
  suppose
    j = k;
    hence thesis;
  end;
end;
