reserve a,b,d,n,k,i,j,x,s for Nat;

theorem Th7:
  Fib 6 = 8 & Fib 7 = 13 & Fib 8 = 21 & Fib 9 = 34 &
  Fib 10 = 55 & Fib 11 = 89 & Fib 12 = 144 & Fib 13 = 233 &
  Fib 14 = 377 & Fib 15 = 610 & Fib 16 = 987 & Fib 17 = 1597 &
  Fib 18 = 2584 & Fib 19 = 4181 & Fib 20 = 6765 & Fib 21 = 10946 &
  Fib 22 = 17711 & Fib 23 = 28657 & Fib 24 = 46368 & Fib 25 = 75025
proof
  A1:Fib(4+1+1) = 5+3 by PRE_FF:1,NUMBER06:46,FIB_NUM2:23;
  then A2:Fib(5+1+1) = 8+5 by NUMBER06:46,PRE_FF:1;
  then A3:Fib(6+1+1) = 13+8 by A1,PRE_FF:1;
  then A4:Fib(7+1+1) = 21+13 by A2,PRE_FF:1;
  then A5:Fib(8+1+1) = 34+21 by A3,PRE_FF:1;
  then A6:Fib(9+1+1) = 55+34 by A4,PRE_FF:1;
  then A7:Fib(10+1+1) = 89+55 by A5,PRE_FF:1;
  then A8:Fib(11+1+1) = 144+89 by A6,PRE_FF:1;
  then A9:Fib(12+1+1) = 233+144 by A7,PRE_FF:1;
  then A10:Fib(13+1+1) = 377+233 by A8,PRE_FF:1;
  then A11:Fib(14+1+1) = 610+377 by A9,PRE_FF:1;
  then A12:Fib(15+1+1) = 987+610 by A10,PRE_FF:1;
  then A13:Fib(16+1+1) = 1597+987 by A11,PRE_FF:1;
  then A14:Fib(17+1+1) = 2584+1597 by A12,PRE_FF:1;
  then A15:Fib(18+1+1) = 4181+2584 by A13,PRE_FF:1;
  then A16:Fib(19+1+1) = 6765+4181 by A14,PRE_FF:1;
  then A17:Fib(20+1+1) = 10946+6765 by A15,PRE_FF:1;
  then A18:Fib(21+1+1) = 17711+10946 by A16,PRE_FF:1;
  then A19:Fib(22+1+1) = 28657+17711 by A17,PRE_FF:1;
  then Fib(23+1+1) = 46368+28657 by A18,PRE_FF:1;
  hence thesis by A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11,A12,A13,A14,A15,
    A16,A17,A18,A19;
end;
