ProofCut.ylen: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 731-740 of lawful-fields@0.1.1.0/proof_cut.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&start_line=731&end_line=740

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

# The slice from s to T has T - s bytes.
law ylen:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +s: Nat
  for +tt: Nat
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +hT: {Nat.is_le(tt, U32.to_nat(len)) == True{} : Bool}
  {List.length(&2, U32, D.slice(D.view(C.BT(len, t)), s, Nat.sub(tt, s))) == Nat.sub(tt, s) : Nat}

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  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=ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=slice
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=view
  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=view_size_t
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&name=take_length
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=drop_length
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=sub_mono