Catalan's Identity/Proof 1

Proof 1
From the initial definition of Fibonacci numbers, we have:
 * $F_1 = 1, F_2 = 1, F_3 = 2, F_4 = 3$

By Fibonacci Numbers in terms of Smaller Fibonacci Numbers:
 * $F_n = F_{n - r} F_{r - 1} + F_{n - r + 1} F_r$

Also:

Therefore: