GatherPROOF.below_inside: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 25-31 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=25&end_line=31

import Base
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws

def below_inside(entries: List<&2, U32>, +bound: Nat) -> {Gather.below(entries, bound) == Laws.inside(entries, bound) : Bool}:
  match entries:
    case Nil{}:
      {==}
    case +head <> rest:
      Equal.cong(Bool, Bool, x => Bool.and(Nat.is_lt(U32.to_nat(head), bound), x), Gather.below(rest, bound), Laws.inside(rest, bound),
        below_inside(rest, bound))

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.cong
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=inside