I searched the forum and couldn't find this proof. I keep getting stuck once I start to substitute. I don't think its that hard, I just can't get past the substitution!!!! Help!!! TIA

Refer to the defnition of Fibonacci numbers F(n)

F(1) = 1

F(2) = 1

F(n) = F(n-1) + F(n-2)

Use strong induction to show that F(n+k) = F(n+1)F(k) + F(n)F(k−1)