LAWS.first_set64_lowest: law of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/LAWS.bend as LAWS
Lines 117-123 of bend-osdev-algo@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/LAWS.bend&start_line=117&end_line=123

import Base
import bend-osdev-word64@0.1.0.0/word64.bend as W
import bend-osdev-algo@0.1.0.0/algo.bend as A

law first_set64_lowest:
  for a: W.W64
  for k: Nat
  for j: Nat
  for e: {A.bits64.first_set(a) == Some{k} : Maybe<&2, Nat>}
  for l: {Nat.is_lt(j, k) == True{} : Bool}
  {A.bits64.test(a, j) == False{} : Bool}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=bitw.first_set_lowest
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bits64.first_set
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bits64.test
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/algo.bend&name=bits64.word
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.1/word64.bend&name=W64