LAWS.size_count: law of lawful-arrays@0.1.0.0
Import: import lawful-arrays@0.1.0.0/LAWS.bend as LAWS
Lines 39-47 of lawful-arrays@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=lawful-arrays@0.1.0.0/LAWS.bend&start_line=39&end_line=47

import Base
import lawful-arrays@0.1.0.0/defs.bend as D

# Array.size doubles 1 once per level of the left spine: for a perfect tree of
# depth d below 32 that is the number of leaves, 2^d.
law size_count:
  for -T: Data
  for a: Array<T>
  for d: Nat
  for hf: {D.full(T, a, d) == True{} : Bool}
  for hd: {Nat.is_lt(d, 32n) == True{} : Bool}
  {U32.to_nat(Pair.snd(Array<T>, U32, Array.size(T, a))) == Nat.pow(2n, d) : Nat}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.size
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/PROOF.bend&name=size_count.go
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/defs.bend&name=full
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=mirror