Standard finite pruned trees

Content created by Jonathan Prieto-Cubides, Egbert Rijke and Fredrik Bakke.

Created on 2022-03-07.
Last modified on 2023-03-13.

module univalent-combinatorics.standard-finite-pruned-trees where
Imports 
open import elementary-number-theory.natural-numbers

open import foundation.universe-levels

open import univalent-combinatorics.standard-finite-types

Idea

A standard finite pruned tree of height n can be thought of as a standard finite tree in which each path from the root to a leaf has length n + 1.

Definition

data Pruned-Tree-Fin : ℕ → UU lzero where
  root-Pruned-Tree-Fin : Pruned-Tree-Fin zero-ℕ
  tree-Pruned-Tree-Fin :
    (n k : ℕ) → (Fin k → Pruned-Tree-Fin n) → Pruned-Tree-Fin (succ-ℕ n)

width-Pruned-Tree-Fin : (n : ℕ) → Pruned-Tree-Fin (succ-ℕ n) → ℕ
width-Pruned-Tree-Fin n (tree-Pruned-Tree-Fin .n k x) = k

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