Canon.is_zero_val: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend as Canon
Lines 165-172 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&start_line=165&end_line=172

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

def is_zero_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}) -> {F.is_zero(x) == Nat.is_eq(Nat.mod(FS.value(x), 1n+pp), 0n) : Bool}:
  +y = F.freeze(x)
  +hy = freeze_okb(one, h1, pp, hP, x, hx)
  +e1 = u32_iz(F.sum_all(y, 0))
  +e2 = Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), v(F.sum_all(y, 0)), sumv(y), sum_v(one, h1, 32n, y, 0, hy, cb32_lt(one, h1)))
  +e3 = iz_sum(y)
  +e4 = Equal.cong(Nat, Bool, z => Nat.is_eq(z, 0n), FS.value(y), Nat.mod(FS.value(x), 1n+pp), freeze_val(one, h1, pp, hP, x, hx))
  Equal.trans(Bool, U32.is_eq(F.sum_all(y, 0), 0), Nat.is_eq(v(F.sum_all(y, 0)), 0n), Nat.is_eq(Nat.mod(FS.value(x), 1n+pp), 0n), e1, Equal.trans(Bool, Nat.is_eq(v(F.sum_all(y, 0)), 0n), Nat.is_eq(sumv(y), 0n), Nat.is_eq(Nat.mod(FS.value(x), 1n+pp), 0n), e2, Equal.trans(Bool, Nat.is_eq(sumv(y), 0n), Nat.is_eq(FS.value(y), 0n), Nat.is_eq(Nat.mod(FS.value(x), 1n+pp), 0n), e3, e4)))

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.cong
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=cb32_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=freeze_okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=freeze_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=iz_sum
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=sum_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=sumv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=u32_iz
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/canon.bend&name=v
  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/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=freeze
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=sum_all