Freeze.cs_val: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend as Freeze
Lines 80-86 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend&start_line=80&end_line=86

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/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/poly.bend as PL
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fold.bend as FD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fieldops.bend as FO

# value(s) + 2^256 c == value(x) + (p + 38)
def cs_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +x: List<&2, U32>, +cp: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +hk: {LM.okb(32n, cp, 128n) == True{} : Bool}, +hv: {K.valo(one, cp) == Nat.add(1n+pp, 38n) : Nat}) -> {Nat.add(FS.value(LM.cl(F.carry(F.addl(x, cp), 0))), LM.shn(32n, v(LM.cc(F.carry(F.addl(x, cp), 0))))) == Nat.add(FS.value(x), Nat.add(1n+pp, 38n)) : Nat}:
  +ys = F.addl(x, cp)
  +e1 = FD.cr_val(one, h1, ys, ad_okb(one, h1, x, cp, hx, hk))
  +e2 = PL.addl_val(one, h1, x, cp, 255n, 128n, LM.okb_lea(32n, x, 255n, hx), LM.okb_lea(32n, cp, 128n, hk), FO.lt32_small(one, h1, Nat.add(255n, 128n), {==}))
  +e3 = Equal.trans(Nat, FS.value(cp), K.valo(one, cp), Nat.add(1n+pp, 38n), Equal.sym(Nat, K.valo(one, cp), FS.value(cp), K.valo_value(one, h1, cp)), hv)
  Equal.trans(Nat, Nat.add(FS.value(LM.cl(F.carry(ys, 0))), LM.shn(32n, v(LM.cc(F.carry(ys, 0))))), FS.value(ys), Nat.add(FS.value(x), Nat.add(1n+pp, 38n)), e1, Equal.trans(Nat, FS.value(ys), Nat.add(FS.value(x), FS.value(cp)), Nat.add(FS.value(x), Nat.add(1n+pp, 38n)), e2, M.cong_r(FS.value(x), FS.value(cp), Nat.add(1n+pp, 38n), e3)))

Uses (23):
  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=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=lt32_small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/fold.bend&name=cr_val
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend&name=ad_okb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/freeze.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=cc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=cl
  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/limbs.bend&name=okb_lea
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=shn
  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/poly.bend&name=addl_val
  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=addl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend&name=carry