Proof.gen_outputs: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/proof.bend as Proof
Lines 32-40 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/proof.bend&start_line=32&end_line=40

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-crypto@1.0.0.0/src/math/random/chacha8.bend as C8
import bend-collections-laws-crypto@1.0.0.0/src/crypto/random.bend as CR
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend as SRC

# the generator's outputs are its ChaCha8's; pending bytes are only for bytes
def gen_outputs(+n: Nat, +c: C8.ChaCha8, +p: List<&2, U32>) -> {SRC.outputs(~CR.Gen, ~CR.next, n, CR.G{c, p}) == SRC.outputs(~C8.ChaCha8, ~C8.next, n, c) : List<&2, W.U64>}:
  match n:
    case 0n:
      {==}
    case 1n+m:
      %Equal.sym(W.U64, SRC.fst64(CR.Gen, CR.keep_pending(p, C8.next(c))), SRC.fst64(C8.ChaCha8, C8.next(c)), kp_fst(p, C8.next(c))) : {Con{_, SRC.outputs(~CR.Gen, ~CR.next, m, SRC.snd64(CR.Gen, CR.keep_pending(p, C8.next(c))))} == SRC.outputs(~C8.ChaCha8, ~C8.next, 1n+m, c) : List<&2, W.U64>}
      %Equal.sym(CR.Gen, SRC.snd64(CR.Gen, CR.keep_pending(p, C8.next(c))), CR.G{SRC.snd64(C8.ChaCha8, C8.next(c)), p}, kp_snd(p, C8.next(c))) : {Con{SRC.fst64(C8.ChaCha8, C8.next(c)), SRC.outputs(~CR.Gen, ~CR.next, m, _)} == SRC.outputs(~C8.ChaCha8, ~C8.next, 1n+m, c) : List<&2, W.U64>}
      Equal.cong(List<&2, W.U64>, List<&2, W.U64>, l => Con{SRC.fst64(C8.ChaCha8, C8.next(c)), l}, SRC.outputs(~CR.Gen, ~CR.next, m, CR.G{SRC.snd64(C8.ChaCha8, C8.next(c)), p}), SRC.outputs(~C8.ChaCha8, ~C8.next, m, SRC.snd64(C8.ChaCha8, C8.next(c))), gen_outputs(m, SRC.snd64(C8.ChaCha8, C8.next(c)), p))

Uses (16):
  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.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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/proof.bend&name=kp_fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/random/proof.bend&name=kp_snd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend&name=fst64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend&name=outputs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend&name=snd64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/random.bend&name=Gen
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/random.bend&name=keep_pending
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/random.bend&name=next
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/chacha8.bend&name=ChaCha8
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/chacha8.bend&name=next
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=U64