reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th91:
  p in rng f implies p in rng Rotate(f,p)
proof
  p in {p} by TARSKI:def 1;
  then p in rng<*p*> by FINSEQ_1:39;
  then p in rng<*p*> \/ rng(f/^p..f) by XBOOLE_0:def 3;
  then p in rng(<*p*>^(f/^p..f)) by FINSEQ_1:31;
  then
A1: p in rng(f:-p) by FINSEQ_5:def 2;
  assume p in rng f;
  then Rotate(f,p) = (f:-p)^((f-:p)/^1) by Def2;
  then rng Rotate(f,p) = rng(f:-p) \/ rng((f-:p)/^1) by FINSEQ_1:31;
  hence thesis by A1,XBOOLE_0:def 3;
end;
