theorem Th9:
  p in rng f & 1 <= i & i <= len(f:-p) implies (Rotate(f,p))/.i = f
  /.(i -' 1 + p..f)
proof
  assume that
A1: p in rng f and
A2: 1 <= i and
A3: i <= len(f:-p);
A4: i in dom(f:-p) by A2,A3,FINSEQ_3:25;
A5: i = i -' 1 + 1 by A2,XREAL_1:235;
  Rotate(f,p) = (f:-p)^((f-:p)/^1) by A1,Def2;
  hence (Rotate(f,p))/.i = (f:-p)/.i by A4,FINSEQ_4:68
    .= f/.(i -' 1 + p..f) by A1,A5,A4,FINSEQ_5:52;
end;
