def mul_e

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarops.bend:152

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

152def mul_e(+one: Nat, +h1: {one == 1n : Nat}, +a: List<&2, Nat>, +b: List<&2, Nat>, +ha: {FS.reduced(one, FS.order(one), a) == True{} : Bool}, +hb: {FS.reduced(one, FS.order(one), b) == True{} : Bool}) -> {LV.ev(S.mul(a, b)) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.np(one)) : Nat}:
153  %Equal.sym(List<&2, Nat>, S.mul(a, b), S.mul_u(a, b), FR.s_mul(a, b)) : {LV.ev(_) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.np(one)) : Nat}
154  %Equal.sym(Nat, LV.ev(S.reduce_u(L.conv(a, b))), Nat.mod(LV.ev(L.conv(a, b)), 1n+K.np(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.np(one)) : Nat}
155  %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.np(one)) == Nat.mod(Nat.mul(LV.ev(a), LV.ev(b)), 1n+K.np(one)) : Nat}
156  {==}