reserve f for non constant standard special_circular_sequence,
  i,j,k,i1,i2,j1,j2 for Nat,
  r,s,r1,s1,r2,s2 for Real,
  p,q for Point of TOP-REAL 2,
  G for Go-board;

theorem Th15:
  1 <= k & k+1 <= len f implies Int right_cell(f,k) <> {}
proof
  assume that
A1: 1 <= k and
A2: k+1 <= len f;
A3: len f = len Rev f by FINSEQ_5:def 3;
  k <= len f by A2,NAT_1:13;
  then
A4: len f-'k+k = len f by XREAL_1:235;
  then
A5: len f-'k+1 <= len f by A1,XREAL_1:6;
A6: len f-'k >= 1 by A2,A4,XREAL_1:6;
  then right_cell(f,k) = left_cell(Rev f,len f-'k) by A1,A4,Th9;
  hence thesis by A3,A5,A6,Th14;
end;
