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 ( 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 ) by A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19; :: thesis: verum