ProofDigits.pd_room: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_digits.bend as ProofDigits
Lines 747-754 of lawful-fields@0.1.1.0/proof_digits.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&start_line=747&end_line=754

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-fields@0.1.1.0/fields.bend as FC
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law pd_room:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +n: U32
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +hc: {Nat.is_le(Nat.add(D.size(C.BT(len, t)), 10n), D.cap(C.BT(len, t))) == True{} : Bool}
  {Nat.is_le(Nat.add(U32.to_nat(len), List.length(&2, U32, FC.put_dec.list(n))), Nat.mul(4n, Nat.pow(2n, d))) == True{} : Bool}

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  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/proof_base.bend&name=subst
  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-bytes@0.1.1.0/defs.bend&name=cap
  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/defs.bend&name=size
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_ops.bend&name=cap_ok_t
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/fields.bend&name=put_dec.list
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=list_len
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_mono_l
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_trans