ProofFastFind2.hv02: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_find2.bend as ProofFastFind2
Lines 188-196 of lawful-bytes@0.1.1.0/proof_fast_find2.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_find2.bend&start_line=188&end_line=196

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-bytes@0.1.1.0/proof_fast_find.bend as FF
import lawful-arrays@0.1.0.0/proof_tree.bend as P

# The next word starts a fresh search.
law hv02:
  for +t: P.Tree<U32>
  for +wi: U32
  for +c1: U32
  for +c2: U32
  for +hc1: {U32.is_lt(c1, 256) == True{} : Bool}
  for +hc2: {U32.is_lt(c2, 256) == True{} : Bool}
  {Nat.min(FW.P0(U32.xor(C.WD(t, wi), FA.rep(c1))), FW.P0(U32.xor(C.WD(t, wi), FA.rep(c2)))) == Nat.add(0n, D.run_len2(FF.AW(t, wi, 0n), c1, c2)) : Nat}

Uses (22):
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.drop
  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.min
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.xor
  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=run_len
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=run_len2
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=rep
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=drop_zero
  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=WD
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find2.bend&name=min_run
  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=hd_eq
  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=p0_xor