Data.Nat.Fib
Properties of the Fibonacci function.
- fibAcc : Nat ->
Nat ->
Nat ->
Nat
Accumulator for fibItr.
- fibAdd : (n : Nat) ->
(a : Nat) ->
(b : Nat) ->
(c : Nat) ->
(d : Nat) ->
fibAcc n
a
b +
fibAcc n
c
d =
fibAcc n
(a +
c)
(b +
d)
Helper lemma for fibacc.
- fibEq : (n : Nat) ->
fibRec n =
fibItr n
Iterative and recursive Fibonacci definitions are equivalent.
- fibItr : Nat ->
Nat
Iterative definition of Fibonacci.
- fibRec : Nat ->
Nat
Recursive definition of Fibonacci.
- plusLemma : (a : Nat) ->
(b : Nat) ->
(c : Nat) ->
(d : Nat) ->
a +
b +
(c +
d) =
a +
c +
(b +
d)
Addend shuffling lemma.