def lt_n_s

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fwrap.bend:60

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/listops.bend as LO

60def lt_n_s(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>) -> {S.lt_n(a) == Nat.is_lt(FS.value(one, a), FS.order(one)) : Bool}:
61  %Equal.sym(Bool, L.ltm(S.c(), a), Nat.is_lt(LV.ev(a), 1n+K.np(one)), LO.ltm_vv(one, h1, K.np(one), S.c(), K.hm_n(one, h1), a)) : {_ == Nat.is_lt(FS.value(one, a), FS.order(one)) : Bool}
62  %Equal.sym(Nat, FS.value(one, a), LV.ev(a), LV.ev_value(one, h1, a)) : {Nat.is_lt(LV.ev(a), 1n+K.np(one)) == Nat.is_lt(_, FS.order(one)) : Bool}
63  %Equal.sym(Nat, FS.order(one), 1n+K.np(one), K.order_eq(one, h1)) : {Nat.is_lt(LV.ev(a), 1n+K.np(one)) == Nat.is_lt(LV.ev(a), _) : Bool}
64  {==}