PROOF.set.root_a: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 692-695 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=692&end_line=695

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

def set.root_a(+i: C.CapSet(), +b: C.CapSet(), +a: C.CapSet()) -> {C.CapSet.subset(a, i) == True{} : Bool} -> {C.CapSet.union(C.CapSet.union(C.CapSet.inter(i, C.CapSet.full()), C.CapSet.inter(C.CapSet.full(), b)), a) == C.CapSet.union(i, b) : C.CapSet()}:
  match i b a:
    case C.CapSetW{U32{+il}, +ih} C.CapSetW{U32{+bl}, +bh} C.CapSetW{U32{+al}, +ah}:
      +h0 => set.eq_intro(Word.or(32n, Word.or(32n, Word.and(32n, il, C.CapBits.all(32n)), Word.and(32n, C.CapBits.all(32n), bl)), al), Word.or(32n, il, bl), Word.or(9n, Word.or(9n, Word.and(9n, ih, C.CapBits.all(9n)), Word.and(9n, C.CapBits.all(9n), bh)), ah), Word.or(9n, ih, bh), bits.root_a(32n, il, bl, al)(set.sub_lo(al, il, ah, ih)(h0)), bits.root_a(9n, ih, bh, ah)(set.sub_hi(al, il, ah, ih)(h0)))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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=bend-osdev-caps@0.1.0.0/PROOF.bend&name=bits.root_a
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.eq_intro
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.sub_hi
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.sub_lo
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapBits.all
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.full
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.inter
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.subset
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSet.union
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapSetW