Final.which0: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend as Final
Lines 305-309 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&start_line=305&end_line=309

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/poly1305/limbs.bend as Li
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U3
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend as V
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend as ST

def which0(+one: Nat, +h1: {one == 1n : Nat}, +h: List<&2, U32>, +hh: {ST.inv(h) == True{} : Bool}, +hc: {Nat.is_eq(qq(h), 0n) == True{} : Bool}) -> {Li.freeze(h) == Li.take(16n, h) : List<&2, U32>}:
  +eb = U3.injective(bb(h), 0, A.tr(V.v(bb(h)), qq(h), 0n, bval(one, h1, h, hh), N.eq_from_is_eq(qq(h), 0n, hc)))
  Equal.trans(List<&2, U32>, Li.freeze(h), Li.select(U32.sub(0, 0), Li.take(16n, h), Li.take(16n, gg(h))), Li.take(16n, h),
    Equal.cong(U32, List<&2, U32>, w => Li.select(U32.sub(0, w), Li.take(16n, h), Li.take(16n, gg(h))), bb(h), 0, eb),
    sel0(Li.take(16n, h), Li.take(16n, gg(h)), heqlen(h, hh)))

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.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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=tr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=bb
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=bval
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=gg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=heqlen
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=qq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/final.bend&name=sel0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend&name=inv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=eq_from_is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=injective
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/poly1305/limbs.bend&name=freeze
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/poly1305/limbs.bend&name=select
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/poly1305/limbs.bend&name=take