PointwiseProof.inside_split: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend as PointwiseProof
Lines 110-122 of bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&start_line=110&end_line=122

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend as Pointwise

def inside_split(~P: Data, ~map: P -> Nat -> Nat, +plan: P, +previous: Nat, +bound: Nat,
  all: {Pointwise.inside(~P, ~map, plan, 1n+previous, bound) == True{} : Bool}, +index: Nat,
  below: {Nat.is_lt(index, 1n+previous) == True{} : Bool},
  rec: {Pointwise.inside(~P, ~map, plan, previous, bound) == True{} : Bool} -> {Nat.is_lt(index, previous) == True{} : Bool} ->
    {Nat.is_lt(map(plan, index), bound) == True{} : Bool},
  decision: Shape.BoolCase<Nat.is_eq(index, previous)>) -> {Nat.is_lt(map(plan, index), bound) == True{} : Bool}:
  match decision:
    case Shape.BTrue{same}:
      %Equal.sym(Nat, index, previous, Lifecycle.natural_equal(index, previous, same)) : {Nat.is_lt(map(plan, _), bound) == True{} : Bool}
      Arith.and_right(Pointwise.inside(~P, ~map, plan, previous, bound), Nat.is_lt(map(plan, previous), bound), all)
    case Shape.BFalse{other}:
      rec(Arith.and_left(Pointwise.inside(~P, ~map, plan, previous, bound), Nat.is_lt(map(plan, previous), bound), all),
        lt_succ_ne(index, previous, below, other))

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=Equal.sym
  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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BoolCase
  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
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=inside
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=lt_succ_ne
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=natural_equal