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 <= width G & 1 <= i & i <= k & k <= len G implies G*(i,j)`1
  <= G*(k,j)`1
proof
  assume that
A1: 1 <= j and
A2: j <= width G and
A3: 1 <= i and
A4: i <= k and
A5: k <= len G;
  per cases by A4,XXREAL_0:1;
  suppose
    i < k;
    hence thesis by A1,A2,A3,A5,GOBOARD5:3;
  end;
  suppose
    i = k;
    hence thesis;
  end;
end;
