Uint64n.step_false: def of bend-collections-laws-crypto@1.0.0.0 Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend as Uint64n Lines 185-192 of bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&start_line=185&end_line=192 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/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 # one retry step, accepted def 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}: +hi = X.psnd(X.mul128(x, n)) +lo = X.pfst(X.mul128(x, n)) +H = C.high(64n, Nat.mul(SW.value(x), 1n+m)) %Equal.sym(R.Draw, 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} %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} Equal.cong(Nat, Nat & S, z => (z, s1), SW.value(hi), H, hi_value(x, n, m, hv)) Uses (31): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=cont https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=fixpoint https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=hd_of https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=hi_value https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=high https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=accept https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=and_bits https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=below_go https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=draw https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=pow2mod https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random.bend&name=val_pair https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend&name=value https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=Draw https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=again https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=result https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=retry https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=U64 https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=lt https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=mul128 https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=pfst https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=psnd