ProofFastAppend.gj: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_append.bend as ProofFastAppend
Lines 625-643 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=625&end_line=643

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

# Byte j of the window at 4 si + r, for j below m.
law gj:
  for +ts: P.Tree<U32>
  for +e: Nat
  for +si: U32
  for +p: U32
  for +lo: U32
  for +r: Nat
  for +m: Nat
  for +j: Nat
  for +hf: {A.full(U32, P.fromT(U32, ts), e) == True{} : Bool}
  for +he: {Nat.is_le(e, 29n) == True{} : Bool}
  for +hlo: {lo == C.WD(ts, si) : U32}
  for +hp: {U32.to_nat(p) == Nat.add(U32.to_nat(si), 1n) : Nat}
  for +hr: {Nat.is_lt(r, 4n) == True{} : Bool}
  for +hm: {Nat.is_le(m, 4n) == True{} : Bool}
  for +hb: {Nat.is_le(Nat.add(Nat.add(Nat.mul(U32.to_nat(si), 4n), r), m), Nat.mul(4n, Nat.pow(2n, e))) == True{} : Bool}
  for +hjm: {Nat.is_lt(j, m) == True{} : Bool}
  {List.get(&2, U32, List.drop(&2, U32, US(ts), Nat.add(Nat.mul(U32.to_nat(si), 4n), r)), j) == Some{W.byte(W.merge(lo, C.WD(ts, p), r), j)} : Maybe<&2, U32>}

Uses (26):
  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=List.drop
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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.is_lt
  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/defs.bend&name=full
  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-arrays@0.1.0.0/proof_tree.bend&name=fromT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=WD
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=US
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=gsel
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=get_drop
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=merge
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_add_l
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans