PROOF.bits.bound_z: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 289-358 of bend-osdev-caps@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&start_line=289&end_line=358

import Base
import bend-osdev-caps@0.1.0.0/caps.bend as C

def bits.bound_z(+n: Nat, +i: Word(n), +fi: Word(n), +fp: Word(n), +b: Word(n), +a: Word(n)) -> {C.CapBits.subset(n, Word.or(n, Word.or(n, Word.and(n, i, fi), Word.and(n, fp, b)), Word.zero(n)), Word.or(n, b, Word.or(n, i, a))) == True{} : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+n1:
      match i fi fp b a:
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{True{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{True{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{True{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{True{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{True{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)
        case WCon{False{}, +it} WCon{False{}, +fit} WCon{False{}, +fpt} WCon{False{}, +bt} WCon{False{}, +at}:
          bits.bound_z(n1, it, fit, fpt, bt, at)

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapBits.subset