Reducek.reduce3_lv: 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 136-140 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=136&end_line=140

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/spec/crypto/secp256k1/field.bend as FS
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/lib/logic.bend as Lg
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV

def reduce3_lv(+one: Nat, +h1: {one == 1n : Nat}, +c: List<&2, Nat>, +hcc: {Nat.is_lt(Nat.add(FS.value(one, c), FS.value(one, c)), C.shift(256n, one)) == True{} : Bool}, +hb: {Nat.is_le(Nat.add(Nat.mul(1n+FS.value(one, c), FS.value(one, c)), FS.value(one, c)), C.shift(256n, one)) == True{} : Bool}, +xs: List<&2, Nat>, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {FS.limbs16(one, 16n, L.reduce(c, 3n, xs)) == True{} : Bool}:
  +e = hv_ev(one, h1, c)
  +hcc2 = Lg.subst(Nat, z => {Nat.is_lt(Nat.add(z, z), C.shift(256n, one)) == True{} : Bool}, FS.value(one, c), LV.ev(c), e, hcc)
  +hb2 = Lg.subst(Nat, z => {Nat.is_le(Nat.add(Nat.mul(1n+z, z), z), C.shift(256n, one)) == True{} : Bool}, FS.value(one, c), LV.ev(c), e, hb)
  reduce3_l(one, h1, c, hcc2, hb2, xs, hx)

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend&name=hv_ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/reducek.bend&name=reduce3_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=limbs16
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=value
  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=reduce