def and_low

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/u32.bend:245

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

245def and_low(+n: Nat, +d: Nat, +x: Word(n), +y: Word(n), +hy: {S.unsigned(n, y) == Nat.sub(SC.pow2(d), 1n) : Nat}, +hx: {Nat.is_lt(S.unsigned(n, x), SC.pow2(d)) == True{} : Bool}) -> {Word.and(n, x, y) == x : Word(n)}:
246  match n:
247    case 0n:
248      match x y:
249        case WNil{} WNil{}:
250          {==}
251    case 1n+m:
252      match x y:
253        case WCon{+xb, +xt} WCon{+yb, +yt}:
254          and_low_step(m, d, xb, xt, yb, yt, hy, hx, and_low(m, and_low_prev(d), xt, yt, and_low_hy(m, d, yb, yt, hy), and_low_hx(m, d, xb, xt, hx)))