def step_true

bend-collections-laws-crypto@1.0.0.0 · proofs/math/random/uint64n.bend:194

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend as SRC
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-crypto@1.0.0.0/spec/math/random.bend as SRM

194# one retry step, rejected: the next draw
195def step_true(~S: Data, ~next: S -> WU.U64 & S, +g: Nat, +n: WU.U64, +m: Nat, +t: WU.U64, +x: WU.U64, +s1: S, +hv: {SW.value(n) == 1n+m : Nat}, +hp: {Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) == False{} : Bool}, +htn: {Nat.is_lt(SR.pow2mod(64n, 1n+m), 1n+m) == True{} : Bool}, +ht: {SW.value(t) == SR.pow2mod(64n, 1n+m) : Nat}, +hc: {X.lt(X.pfst(X.mul128(x, n)), t) == True{} : Bool}, +rec: {SRM.val_pair(S, R.result(S, R.retry(~S, ~next, g, n, t, R.draw(S, n, next(s1))))) == cont(~S, ~next, g, 1n+m, SW.value(SRC.fst64(S, next(s1))), SRC.snd64(S, next(s1))) : Nat & S}) -> {SRM.val_pair(S, R.result(S, R.retry(~S, ~next, g, n, t, R.again(~S, ~next, n, X.psnd(X.mul128(x, n)), X.pfst(X.mul128(x, n)), s1, True{})))) == cont(~S, ~next, 1n+g, 1n+m, SW.value(x), s1) : Nat & S}:
196  +H = C.high(64n, Nat.mul(SW.value(x), 1n+m))
197  %Equal.sym(Maybe<&2, Nat>, SR.draw(64n, SW.value(x), 1n+m), SR.accept(H, False{}), hd_of(x, n, m, t, hv, hp, htn, ht, True{}, hc)) : {SRM.val_pair(S, R.result(S, R.retry(~S, ~next, g, n, t, R.draw(S, n, next(s1))))) == SR.below_go(~S, ~next, 1n+g, 1n+m, _, SW.value(x), s1) : Nat & S}
198  rec