ProofFastFind.fhit: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_find.bend as ProofFastFind
Lines 506-523 of lawful-bytes@0.1.1.0/proof_fast_find.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&start_line=506&end_line=523

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/fast.bend as FA
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-bytes@0.1.1.0/proof_fast_word.bend as FW
import lawful-arrays@0.1.0.0/proof_tree.bend as P

# The flagged word: the answer is the first c from the start, or to.
law fhit:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +to: U32
  for +c: U32
  for +wi: U32
  for +o: Nat
  for +v: U32
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +ht: {Nat.is_le(U32.to_nat(to), U32.to_nat(len)) == True{} : Bool}
  for +ho: {Nat.is_lt(o, 4n) == True{} : Bool}
  for +hs: {Nat.is_le(SS(wi, o), U32.to_nat(to)) == True{} : Bool}
  for +hk: {Nat.is_lt(U32.to_nat(wi), Nat.pow(2n, d)) == True{} : Bool}
  for +hv: {FW.P0(v) == Nat.add(o, D.run_len(AW(t, wi, o), c)) : Nat}
  for +hz: {U32.is_zero(FA.zb(v)) == False{} : Bool}
  {U32.to_nat(U32.min(((wi << 2n : U32) + FA.bidx(FA.zb(v)) : U32), to)) == D.first(UB(t), SS(wi, o), U32.to_nat(to), c) : Nat}

Uses (60):
  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=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.length
  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_eq
  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.min
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.min
  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.to_nat
  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-bytes@0.1.1.0/defs.bend&name=first
  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=run_len
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=bidx
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=zb
  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_core.bend&name=L4
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=add_fits
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=ok_d
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=ok_full
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=AW
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=BW
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=SS
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=UB
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=awl
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=dw
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=hd_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=lt_cancel
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=min_shift
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=run_hit
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=run_le
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=shl2
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=wb4
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=P0
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=zb_bidx
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=zb_none
  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=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_ne
  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=le_succ_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_trans
  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_u32.bend&name=to_nat_min