def mul_e

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/fieldops.bend:180

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/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/fprot.bend as FR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K

180def mul_e(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.prime(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {LV.ev(F.mul(a, b)) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.pp(one)) : Nat}:
181  %Equal.sym(List<&2, Nat>, F.mul(a, b), F.mul_u(a, b), FR.f_mul(a, b)) : {LV.ev(_) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.pp(one)) : Nat}
182  %Equal.sym(Nat, LV.ev(F.reduce(L.conv(a, b))), Nat.mod(LV.ev(L.conv(a, b)), 1n+K.pp(one)), red_e(one, h1, L.conv(a, b), mul_hx(one, h1, a, b, ha, hb))) : {_ == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.pp(one)) : Nat}
183  %Equal.sym(Nat, LV.ev(L.conv(a, b)), Nat.mul(LV.ev(a), LV.ev(b)), LV.conv_v(a, b)) : {Nat.mod(_, 1n+K.pp(one)) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.pp(one)) : Nat}
184  {==}