Reducek.red3_x3: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend as Reducek
Lines 31-43 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend&start_line=31&end_line=43

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend as R

def red3_x3(+one: Nat, +h1: {one == 1n : Nat}, +c: List<&2, Nat>, +xs: List<&2, Nat>, +hb: {Nat.is_le(Nat.add(Nat.mul(1n+LV.ev(c), LV.ev(c)), LV.ev(c)), C.shift(256n, one)) == True{} : Bool}, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {Nat.is_lt(LV.ev(L.rounds(3n, c, L.carry(32n, xs, 0n))), C.shift(256n, one)) == True{} : Bool}:
  +t = C.shift(256n, one)
  +cv = LV.ev(c)
  +x0 = L.carry(32n, xs, 0n)
  +x1 = L.carry(32n, L.fold(c, x0), 0n)
  +x2 = L.carry(32n, L.fold(c, x1), 0n)
  +h0 = I.lt_subst_l(LV.ev(xs), LV.ev(x0), Nat.mul(t, t), Equal.sym(Nat, LV.ev(x0), LV.ev(xs), LV.carry_v(32n, xs, 0n)), hx)
  +h1b = R.round_lt1(one, h1, c, x0, t, x0_lo(one, h1, xs), h0)
  +h1c = I.lt_subst_r(LV.ev(x1), Nat.add(t, Nat.mul(t, cv)), Nat.mul(1n+cv, t), addmul(t, cv), h1b)
  +h2b = R.round_lt1(one, h1, c, x1, 1n+cv, R.round_lo(one, h1, L.fold(c, x0)), h1c)
  +h3 = R.fold_lt2(one, h1, c, x2, Nat.mul(1n+cv, cv), hb, R.round_lo(one, h1, L.fold(c, x1)), h2b)
  %Equal.sym(Nat, LV.ev(L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n)), 0n)), LV.ev(L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n))), R.round_v(c, L.carry(32n, L.fold(c, L.carry(32n, L.fold(c, L.carry(32n, xs, 0n)), 0n)), 0n))) : {Nat.is_lt(_, C.shift(256n, one)) == True{} : Bool}
  h3

Uses (22):
  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=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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=lt_subst_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=lt_subst_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=carry_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=fold_lt2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=round_lo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=round_lt1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reduce.bend&name=round_v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend&name=addmul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend&name=x0_lo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=carry
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=fold
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=rounds