Memory.tree_perfect: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend as Memory
Lines 93-98 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&start_line=93&end_line=98

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

def tree_perfect(+d: Nat, +ws: List<&2, U32>) -> {AR.perfect(U32, d, tree(d, ws)) == True{} : Bool}:
  match d:
    case 0n:
      {==}
    case 1n+ +p:
      L.and_intro(AR.perfect(U32, p, tree(p, SC.take(U32, ws, SC.pow2(p)))), AR.perfect(U32, p, tree(p, SC.drop(U32, ws, SC.pow2(p)))), tree_perfect(p, SC.take(U32, ws, SC.pow2(p))), tree_perfect(p, SC.drop(U32, ws, SC.pow2(p))))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/memory.bend&name=tree
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/array.bend&name=perfect
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take