PROOF.set.sub_intro: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 143-147 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=143&end_line=147

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

# a set within another, from its parts within theirs, and back
def set.sub_intro(+al: Word(32n), +bl: Word(32n), +ah: Word(9n), +bh: Word(9n)) -> {C.CapBits.subset(32n, al, bl) == True{} : Bool} -> {C.CapBits.subset(9n, ah, bh) == True{} : Bool} -> {C.CapSet.subset(C.CapSetW{U32{al}, ah}, C.CapSetW{U32{bl}, bh}) == True{} : Bool}:
  hl => hh =>
    %Equal.sym(Bool, Cmp.is_eq(Word.cmp(32n, Word.and(32n, al, Word.not(32n, bl)), Word.zero(32n))), C.CapBits.subset(32n, al, bl), set.bridge(32n, al, bl)) : {Bool.and(_, C.CapBits.subset(9n, ah, bh)) == True{} : Bool}
    bool.and2(C.CapBits.subset(32n, al, bl), C.CapBits.subset(9n, ah, bh))(hl)(hh)

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=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.not
  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/PROOF.bend&name=bool.and2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.bridge
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapBits.subset
  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=CapSetW