def red_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldops.bend:68

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/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
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

68def red_v(+one: Nat, +h1: {one == 1n : Nat}, +xs: List<&2, Nat>, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {FS.value(one, F.reduce(xs)) == Nat.mod(LV.ev(xs), FS.prime(one)) : Nat}:
69  %Equal.sym(Nat, FS.value(one, F.reduce(xs)), LV.ev(F.reduce(xs)), LV.ev_value(one, h1, F.reduce(xs))) : {_ == Nat.mod(LV.ev(xs), FS.prime(one)) : Nat}
70  %Equal.sym(Nat, LV.ev(F.reduce(xs)), Nat.mod(LV.ev(xs), 1n+K.pp(one)), red_e(one, h1, xs, hx)) : {_ == Nat.mod(LV.ev(xs), FS.prime(one)) : Nat}
71  %Equal.sym(Nat, 1n+K.pp(one), FS.prime(one), Equal.sym(Nat, FS.prime(one), 1n+K.pp(one), K.prime_eq(one, h1))) : {Nat.mod(LV.ev(xs), _) == Nat.mod(LV.ev(xs), FS.prime(one)) : Nat}
72  {==}