def mok_odd

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64mont.bend:348

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/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/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sqrt.bend as W64S

348def mok_odd(+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}) -> {Nat.mod(1n+bp, 2n) == 1n : Nat}:
349  +h = Equal.trans(Bool, Nat.is_eq(Nat.mod(SW.value(WU.U64{ml, mh}), 2n), 1n), X.odd(WU.U64{ml, mh}), True{}, Equal.sym(Bool, X.odd(WU.U64{ml, mh}), Nat.is_eq(Nat.mod(SW.value(WU.U64{ml, mh}), 2n), 1n), WA.odd_value(WU.U64{ml, mh})), W64S.and_l(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)))
350  Equal.trans(Nat, Nat.mod(1n+bp, 2n), Nat.mod(SW.value(WU.U64{ml, mh}), 2n), 1n, Equal.cong(Nat, Nat, z => Nat.mod(z, 2n), 1n+bp, SW.value(WU.U64{ml, mh}), Equal.sym(Nat, SW.value(WU.U64{ml, mh}), 1n+bp, hM)), N.eq_from_is_eq(Nat.mod(SW.value(WU.U64{ml, mh}), 2n), 1n, h))