def mok_inv

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64mont.bend:362

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/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend as W64S

362def mok_inv(+one: Nat, +h1: {one == 1n : Nat}, +bp: Nat, +ml: U32, +mh: U32, +hM: {SW.value(WU.U64{ml, mh}) == 1n+bp : Nat}, +hok: {X.mont_ok(WU.U64{ml, mh}) == True{} : Bool}) -> {1n+C.low(64n, Nat.mul(1n+bp, SW.value(X.minv(WU.U64{ml, mh})))) == C.shift(64n, one) : Nat}:
363  mok_inv_o(one, h1, bp, ml, mh, hM, 4294967295, {==}, W64S.and_r(X.odd(WU.U64{ml, mh}), X.eq(X.mul(WU.U64{ml, mh}, X.minv(WU.U64{ml, mh})), WU.U64{4294967295, 4294967295}), mok_ab(ml, mh, hok)))