SlicePROOF.cover: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 206-212 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=206&end_line=212

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_fiber_proof.bend as Fiber

def cover(+rest: Nat, +step: Nat, positive: {Nat.is_lt(0n, step) == True{} : Bool}) ->
  {Nat.is_le(1n+rest, Nat.add(step, Nat.mul(Nat.div(rest, step), step))) == True{} : Bool}:
  match step:
    case 0n:
      Empty.absurd({Nat.is_le(1n+rest, Nat.add(0n, Nat.mul(Nat.div(rest, 0n), 0n))) == True{} : Bool}, Arith.clash(positive))
    case 1n+s:
      covered(rest, s, Fiber.decompose(rest, 1n+s, {==}))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.div
  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=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&name=decompose
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&name=covered