theorem Th21:
  RightComp f = LeftComp Rev f
proof
  LeftComp Rev f is_a_component_of (L~Rev f)` by Def1;
  then
A1: LeftComp Rev f is_a_component_of (L~f)` by SPPOL_2:22;
A2: len f >= 4 by GOBOARD7:34;
A3: len f >= 1+1 by GOBOARD7:34,XXREAL_0:2;
A4: len f -' 1 + 1 = len f by A2,XREAL_1:235,XXREAL_0:2;
  then
A5: 1 <= len f -' 1 by A3,XREAL_1:6;
A6: len f -' 1 + 1 <= len Rev f by A4,FINSEQ_5:def 3;
  right_cell(f,1) = left_cell(Rev f,len f -' 1) by A4,A5,Th9;
  then Int right_cell(f,1) c= LeftComp Rev f by A5,A6,Th19;
  hence thesis by A1,Def2;
end;
