ReduceReplayedProof.below_front: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend as ReduceReplayedProof
Lines 422-432 of bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&start_line=422&end_line=432

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend as ReduceParallel

def below_front(+xs: List<&2, Nat>, +ys: List<&2, Nat>, +bound: Nat,
  +h: {ReduceParallel.all_below(List.append(&2, Nat, xs, ys), bound) == True{} : Bool}) ->
  {ReduceParallel.all_below(xs, bound) == True{} : Bool}:
  match xs:
    case Nil{}:
      {==}
    case +x <> +rest:
      +here = Arith.and_left(Nat.is_lt(x, bound), ReduceParallel.all_below(List.append(&2, Nat, rest, ys), bound), h)
      +later = Arith.and_right(Nat.is_lt(x, bound), ReduceParallel.all_below(List.append(&2, Nat, rest, ys), bound), h)
      %Equal.sym(Bool, Nat.is_lt(x, bound), True{}, here) : {Bool.and(_, ReduceParallel.all_below(rest, bound)) == True{} : Bool}
      below_front(rest, ys, bound, later)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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=List.append
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend&name=all_below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=and_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=and_right