ProofAppend.read_next: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_append.bend as ProofAppend
Lines 234-242 of lawful-bytes@0.1.1.0/proof_append.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&start_line=234&end_line=242

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

law read_next:
  for +ls: U32
  for +ts: P.Tree<U32>
  for +e: Nat
  for +s: U32
  for +k: Nat
  for +he: {D.ok(C.BT(ls, ts), e) == True{} : Bool}
  for +hs: {Nat.is_le(Nat.add(U32.to_nat(s), 1n+k), U32.to_nat(ls)) == True{} : Bool}
  {Nat.is_le(Nat.add(U32.to_nat((s + 1 : U32)), k), U32.to_nat(ls)) == True{} : Bool}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  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_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/proof_append.bend&name=le_shift
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=read_inc
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT