PROOF.AP.mask_lt: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 908-926 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=908&end_line=926

import Base
import bend-osdev-array@0.1.0.1/array.bend as A
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# a word masked to its low d bits is below 2^d
def AP.mask_lt(n: Nat, w: Word(n), +d: Nat) -> {Nat.is_lt(Word.to_nat(n, Word.and(n, w, AP.lm(n, d))), A.Arrays.slots(d)) == True{} : Bool}:
  match n:
    case 0n:
      AP.slots_pos(d)
    case 1n+ +q:
      match w d:
        case WCon{False{}, +t} 0n:
          %Equal.sym(Word(q), Word.and(q, t, Word.zero(q)), Word.zero(q), AP.and_zero(q, t)) : {Nat.is_lt(Nat.double(Word.to_nat(q, _)), 1n) == True{} : Bool}
          %Equal.sym(Nat, Word.to_nat(q, Word.zero(q)), 0n, UL.word_zero_value(q)) : {Nat.is_lt(Nat.double(_), 1n) == True{} : Bool}
          {==}
        case WCon{True{}, +t} 0n:
          %Equal.sym(Word(q), Word.and(q, t, Word.zero(q)), Word.zero(q), AP.and_zero(q, t)) : {Nat.is_lt(Nat.double(Word.to_nat(q, _)), 1n) == True{} : Bool}
          %Equal.sym(Nat, Word.to_nat(q, Word.zero(q)), 0n, UL.word_zero_value(q)) : {Nat.is_lt(Nat.double(_), 1n) == True{} : Bool}
          {==}
        case WCon{False{}, +t} 1n+ +e:
          AP.lt_bv(False{}, Word.to_nat(q, Word.and(q, t, AP.lm(q, e))), A.Arrays.slots(e), AP.mask_lt(q, t, e))
        case WCon{True{}, +t} 1n+ +e:
          AP.lt_bv(True{}, Word.to_nat(q, Word.and(q, t, AP.lm(q, e))), A.Arrays.slots(e), AP.mask_lt(q, t, e))

Uses (16):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.and_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lt_bv
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.slots_pos
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=word_zero_value