ProofFastAppend.avf: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_append.bend as ProofFastAppend
Lines 837-872 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=837&end_line=872

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

# The last word, when fewer than 4 bytes are left.
law avf:
  for +k1: Nat
  for +ts: P.Tree<U32>
  for +e: Nat
  for +td: P.Tree<U32>
  for +d: Nat
  for +p: U32
  for +lo: U32
  for +si: U32
  for +di: U32
  for +sh: Nat
  for +l1: Nat
  for +qn: Nat
  for +r: Nat
  for +o: Nat
  for +np: Nat
  for +v1: List<&2, U32>
  for +hbq: {Nat.is_le(Nat.add(o, 4n), np) == False{} : Bool}
  for +hfs: {A.full(U32, P.fromT(U32, ts), e) == True{} : Bool}
  for +hes: {Nat.is_le(e, 29n) == True{} : Bool}
  for +hfd: {A.full(U32, P.fromT(U32, td), d) == True{} : Bool}
  for +hdd: {Nat.is_le(d, 29n) == True{} : Bool}
  for +hdi: {Nat.mul(U32.to_nat(di), 4n) == Nat.add(l1, o) : Nat}
  for +hsi: {Nat.add(Nat.mul(U32.to_nat(si), 4n), r) == Nat.add(qn, o) : Nat}
  for +hp: {U32.to_nat(p) == Nat.add(U32.to_nat(si), 1n) : Nat}
  for +hlo: {lo == C.WD(ts, si) : U32}
  for +hsh: {sh == Nat.mul(8n, r) : Nat}
  for +hr: {Nat.is_lt(r, 4n) == True{} : Bool}
  for +hq: {Nat.is_le(Nat.add(qn, np), Nat.mul(4n, Nat.pow(2n, e))) == True{} : Bool}
  for +hl: {Nat.is_le(Nat.add(l1, np), Nat.mul(4n, Nat.pow(2n, d))) == True{} : Bool}
  for +hon: {Nat.is_le(o, np) == True{} : Bool}
  for +hc1: {Nat.is_le(np, Nat.add(o, Nat.mul(1n+k1, 4n))) == True{} : Bool}
  for +hc2: {Nat.is_lt(Nat.add(o, Nat.mul(1n+k1, 4n)), Nat.add(np, 4n)) == True{} : Bool}
  for +hinv: {List.take(&2, U32, US(td), Nat.add(l1, o)) == List.append(&2, U32, v1, List.take(&2, U32, List.drop(&2, U32, US(ts), qn), o)) : List<&2, U32>}
  {List.take(&2, U32, US(AWT(1n+k1, ts, p, lo, td, si, di, sh)), Nat.add(l1, np)) == List.append(&2, U32, v1, List.take(&2, U32, List.drop(&2, U32, US(ts), qn), np)) : List<&2, U32>}

Uses (39):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  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.take
  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=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.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  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=false_ne_true
  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_index.bend&name=set_tree
  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=AWT
  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=c4
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=step
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_append.bend&name=sub_le_of
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_mono_l
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_lt_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_sub_add
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_to_le
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=not_le_lt