def step_false

bend-collections-laws-math@1.0.0.0 · proofs/math/random/uint64n.bend:185

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
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/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/spec/math/random.bend as SRM

185# one retry step, accepted
186def step_false(~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) == False{} : Bool}) -> {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, False{})))) == cont(~S, ~next, 1n+g, 1n+m, SW.value(x), s1) : Nat & S}:
187  +hi = X.psnd(X.mul128(x, n))
188  +lo = X.pfst(X.mul128(x, n))
189  +H = C.high(64n, Nat.mul(SW.value(x), 1n+m))
190  %Equal.sym(R.Draw<S>, R.retry(~S, ~next, g, n, t, R.D{hi, lo, s1}), R.D{hi, lo, s1}, fixpoint(~S, ~next, g, n, t, hi, lo, s1, hc)) : {SRM.val_pair(S, R.result(S, _)) == cont(~S, ~next, 1n+g, 1n+m, SW.value(x), s1) : Nat & S}
191  %Equal.sym(Maybe<&2, Nat>, SR.draw(64n, SW.value(x), 1n+m), SR.accept(H, True{}), hd_of(x, n, m, t, hv, hp, htn, ht, False{}, hc)) : {(SW.value(hi), s1) == SR.below_go(~S, ~next, 1n+g, 1n+m, _, SW.value(x), s1) : Nat & S}
192  Equal.cong(Nat, Nat & S, z => (z, s1), SW.value(hi), H, hi_value(x, n, m, hv))