theorem Th21:
  1 <= k & k+1 <= len f & f is_sequence_on G & [i,j+1] in Indices
  G & [i,j] in Indices G & f/.k = G*(i,j+1) & f/.(k+1) = G*(i,j) implies
  right_cell(f,k,G) = cell(G,i-'1,j)
proof
A1: j < j+1 & j+1 <= j+1+1 by XREAL_1:29;
  assume 1 <= k & k+1 <= len f & f is_sequence_on G & [i,j+1] in Indices G &
  [i,j] in Indices G & f/.k = G*(i,j+1) & f/.(k+1) = G*(i,j);
  hence thesis by A1,Def1;
end;
