ProofCut.cut_eq: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_cut.bend as ProofCut
Lines 698-705 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=698&end_line=705

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-fields@0.1.1.0/fields.bend as K
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 cut_eq:
  for +len: U32
  for +t: P.Tree<U32>
  for +from: U32
  for +to: U32
  for +sep: U32
  for +n: Nat
  {K.cut(C.BT(len, t), from, to, sep, n) == (C.BT(len, t), CG(n, True{}, NX(Bool.not(Nat.is_eq(n, 0n)), len, t, from, to, sep), len, t, to, sep)) : D.Bytes & List<&2, U32>}

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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=Bytes
  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-fields@0.1.1.0/fields.bend&name=cut
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/fields.bend&name=cut.go
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/fields.bend&name=cut.next
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=CG
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=NX
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=cg_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_cut.bend&name=nx_eq