reserve n, k, r, m, i, j for Nat;

theorem Th60:
  OddFibs (1) = <*1*>
proof
  now
    let x be object;
    assume
A1: x in {1};
    then x = 2 * (0 qua Nat) + 1 by TARSKI:def 1;
    then x in OddNAT;
    hence x in OddNAT /\ {1} by A1,XBOOLE_0:def 4;
  end;
  then
A2: {1} c= OddNAT /\ {1};
  1 in NAT;
  then
A3: 1 in dom FIB by FUNCT_2:def 1;
  for x be object st x in OddNAT /\ {1} holds x in {1} by XBOOLE_0:def 4;
  then OddNAT /\ {1} c= {1};
  then OddNAT /\ {1} = {1} by A2;
  then OddFibs (1) = <*FIB.1*> by A3,FINSEQ_1:2,FINSEQ_3:157,GRFUNC_1:28
    .= <*1*> by Def2,PRE_FF:1;
  hence thesis;
end;
