ProofCore.ok_mk: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_core.bend as ProofCore
Lines 272-280 of lawful-bytes@0.1.1.0/proof_core.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&start_line=272&end_line=280

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-arrays@0.1.0.0/defs.bend as A
import lawful-arrays@0.1.0.0/proof_tree.bend as P

# ok from its three parts.
law ok_mk:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +hf: {A.full(U32, P.fromT(U32, t), d) == True{} : Bool}
  for +hd: {Nat.is_le(d, 29n) == True{} : Bool}
  for +hl: {Nat.is_le(U32.to_nat(len), Nat.mul(4n, Nat.pow(2n, d))) == True{} : Bool}
  {D.ok(BT(len, t), d) == True{} : Bool}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  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/defs.bend&name=full
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=fromT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT