Fieldops.subg_mod: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as Fieldops
Lines 155-160 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&start_line=155&end_line=160

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/num.bend as M
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/reduce.bend as RD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend as K

def subg_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>, +ks: List<&2, U32>, +ha: {LM.okb(32n, a, 255n) == True{} : Bool}, +hb: {LM.okb(32n, b, 255n) == True{} : Bool}, +hk: {LM.okb(32n, ks, 2040n) == True{} : Bool}, +hg: {gea(ks, 255n) == True{} : Bool}, +hv: {K.valo(one, ks) == Nat.mul(8n, 1n+pp) : Nat}) -> {Nat.mod(FS.value(F.reduce(F.subl(a, b, ks))), 1n+pp) == Nat.mod(Nat.sub(Nat.add(FS.value(a), 1n+pp), Nat.mod(FS.value(b), 1n+pp)), 1n+pp) : Nat}:
  +e1 = RD.reduce_mod(one, h1, pp, hP, F.subl(a, b, ks), subg_okb(one, h1, a, b, ks, ha, hb, hk, hg))
  +es = subl_val(one, h1, 32n, a, b, ks, 255n, 255n, 2040n, ha, hb, hk, hg, lt32_small(one, h1, Nat.add(255n, 2040n), {==}))
  +ek = Equal.trans(Nat, FS.value(ks), K.valo(one, ks), Nat.mul(8n, 1n+pp), Equal.sym(Nat, K.valo(one, ks), FS.value(ks), K.valo_value(one, h1, ks)), hv)
  +hS = Equal.trans(Nat, Nat.add(FS.value(F.subl(a, b, ks)), FS.value(b)), Nat.add(FS.value(a), FS.value(ks)), Nat.add(FS.value(a), Nat.mul(8n, 1n+pp)), es, M.cong_r(FS.value(a), FS.value(ks), Nat.mul(8n, 1n+pp), ek))
  Equal.trans(Nat, Nat.mod(FS.value(F.reduce(F.subl(a, b, ks))), 1n+pp), Nat.mod(FS.value(F.subl(a, b, ks)), 1n+pp), Nat.mod(Nat.sub(Nat.add(FS.value(a), 1n+pp), Nat.mod(FS.value(b), 1n+pp)), 1n+pp), e1, sub_core(pp, FS.value(a), FS.value(b), FS.value(F.subl(a, b, ks)), hS))

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend&name=valo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend&name=valo_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=gea
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=lt32_small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=sub_core
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=subg_okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend&name=subl_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend&name=cong_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/reduce.bend&name=reduce_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=reduce
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=subl