PROOF.set.bridge: def of bend-osdev-caps@0.1.0.0
Import: import bend-osdev-caps@0.1.0.0/PROOF.bend as PROOF
Lines 130-141 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=130&end_line=141

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

def set.bridge(+n: Nat, +x: Word(n), +y: Word(n)) -> {Cmp.is_eq(Word.cmp(n, Word.and(n, x, Word.not(n, y)), Word.zero(n))) == C.CapBits.subset(n, x, y) : Bool}:
  match n:
    case 0n:
      {==}
    case 1n+p:
      match x y:
        case WCon{True{}, +xt} WCon{True{}, +yt}:
          Equal.trans(Bool, Cmp.is_eq(Word.cmp.fin(False{}, False{}, Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p)))), Cmp.is_eq(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p))), C.CapBits.subset(p, xt, yt), set.fin_ff(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p))), set.bridge(p, xt, yt))
        case WCon{True{}, +xt} WCon{False{}, +yt}:
          set.fin_tf(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p)))
        case WCon{False{}, +xt} WCon{+yb, +yt}:
          Equal.trans(Bool, Cmp.is_eq(Word.cmp.fin(False{}, False{}, Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p)))), Cmp.is_eq(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p))), C.CapBits.subset(p, xt, yt), set.fin_ff(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p))), set.bridge(p, xt, yt))

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.trans
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp.fin
  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=set.fin_ff
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/PROOF.bend&name=set.fin_tf
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-caps@0.1.0.0/caps.bend&name=CapBits.subset