def sub_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:171

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend as K

171def sub_mod(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +a: List<&2, U32>, +b: List<&2, U32>, +ha: {LM.okb(32n, a, 255n) == True{} : Bool}, +hb: {LM.okb(32n, b, 255n) == True{} : Bool}) -> {Nat.mod(FS.value(F.sub(a, b)), 1n+pp) == Nat.mod(Nat.sub(Nat.add(FS.value(a), 1n+pp), Nat.mod(FS.value(b), 1n+pp)), 1n+pp) : Nat}:
172  subg_mod(one, h1, pp, hP, a, b, F.eight_p(), ha, hb, eight_p_okb(), eight_p_gea(), K.eight_p_val(one, h1, pp, hP))