def count_mask

bend-collections-laws-crypto@1.0.0.0 · proofs/math/random/lemire.bend:580

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR

580def count_mask(+w: Nat, +m: Nat, +k: Nat, +N: Nat, +hp: {Nat.is_eq(SR.and_bits(w, 1n+m, m), 0n) == True{} : Bool}) -> {SR.count(w, 1n+m, k, N) == cm(w, m, k, N) : Nat}:
581  match N:
582    case 0n:
583      {==}
584    case 1n+ +x:
585      %Equal.sym(Nat, SR.count(w, 1n+m, k, x), cm(w, m, k, x), count_mask(w, m, k, x, hp)) : {Nat.add(_, SR.hit(SR.draw(w, x, 1n+m), k)) == Nat.add(cm(w, m, k, x), b2n(Nat.is_eq(SR.and_bits(w, x, m), k))) : Nat}
586      %Equal.sym(Maybe<&2, Nat>, SR.draw(w, x, 1n+m), Some{SR.and_bits(w, x, m)}, draw_mask(w, m, x, hp)) : {Nat.add(cm(w, m, k, x), SR.hit(_, k)) == Nat.add(cm(w, m, k, x), b2n(Nat.is_eq(SR.and_bits(w, x, m), k))) : Nat}
587      {==}