def set.bridge

bend-osdev-caps@0.1.0.0 · PROOF.bend:130

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

130def 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}:
131  match n:
132    case 0n:
133      {==}
134    case 1n+p:
135      match x y:
136        case WCon{True{}, +xt} WCon{True{}, +yt}:
137          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))
138        case WCon{True{}, +xt} WCon{False{}, +yt}:
139          set.fin_tf(Word.cmp(p, Word.and(p, xt, Word.not(p, yt)), Word.zero(p)))
140        case WCon{False{}, +xt} WCon{+yb, +yt}:
141          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))