ProofFastAppend.el1: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_append.bend as ProofFastAppend
Lines 1331-1344 of lawful-bytes@0.1.1.0/proof_fast_append.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&start_line=1331&end_line=1344

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 el1:
  for +ld: U32
  for +td: P.Tree<U32>
  for +ls: U32
  for +ts: P.Tree<U32>
  for +d: Nat
  for +s: U32
  for +n: U32
  for +l1: U32
  for +t1: P.Tree<U32>
  for +e1: {C.BT(l1, t1) == D1(ld, td, ls, ts, s, n) : D.Bytes}
  for +hd: {D.ok(C.BT(ld, td), d) == True{} : Bool}
  for +hc: {Nat.is_le(Nat.add(D.size(C.BT(ld, td)), U32.to_nat(n)), D.cap(C.BT(ld, td))) == True{} : Bool}
  {U32.to_nat(l1) == Nat.add(U32.to_nat(ld), U32.to_nat(HH(ld, n))) : Nat}

Uses (18):
  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.trans
  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.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=Bytes
  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_fast_append.bend&name=D1
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=HH
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=ag_size
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=hc_h