def value_nz

bend-collections-laws-math@1.0.0.0 · proofs/math/random/uint64n.bend:299

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-math@1.0.0.0/spec/math/random/source.bend as SRC
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as LE
import bend-collections-laws-math@1.0.0.0/spec/math/random.bend as SRM

299def value_nz(~S: Data, ~next: S -> WU.U64 & S, +one: Nat, +h1: {one == 1n : Nat}, +s: S, +n: WU.U64, +m: Nat, +hv: {SW.value(n) == 1n+m : Nat}, +hz: {X.is_zero(n) == False{} : Bool}, +c: Bool, +hc: {Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) == c : Bool}) -> {SRM.val_pair(S, R.uint64n_pick(~S, ~next, s, n, c)) == SR.below(~S, ~next, 127n, 1n+m, s) : Nat & S}:
300  match c:
301    case True{}:
302      +x = SW.value(SRC.fst64(S, next(s)))
303      Equal.trans(Nat & S, SRM.val_pair(S, R.mask(S, n, next(s))), (SR.and_bits(64n, x, m), SRC.snd64(S, next(s))), SR.below(~S, ~next, 127n, 1n+m, s),
304        mask_pair(S, n, m, next(s), hv),
305        %Equal.sym(Maybe<&2, Nat>, SR.draw(64n, x, 1n+m), Some{SR.and_bits(64n, x, m)}, LE.draw_mask(64n, m, x, hc)) : {(SR.and_bits(64n, x, m), SRC.snd64(S, next(s))) == SR.below_go(~S, ~next, 127n, 1n+m, _, x, SRC.snd64(S, next(s))) : Nat & S}
306        {==})
307    case False{}:
308      Equal.trans(Nat & S, SRM.val_pair(S, R.lemire_first(~S, ~next, n, R.draw(S, n, next(s)))), cont(~S, ~next, 127n, 1n+m, SW.value(SRC.fst64(S, next(s))), SRC.snd64(S, next(s))), SR.below(~S, ~next, 127n, 1n+m, s),
309        top_first(~S, ~next, one, h1, n, m, next(s), hv, hz, hc),
310        Equal.sym(Nat & S, SR.below(~S, ~next, 127n, 1n+m, s), cont(~S, ~next, 127n, 1n+m, SW.value(SRC.fst64(S, next(s))), SRC.snd64(S, next(s))), below_cont(~S, ~next, 127n, 1n+m, s)))