ReduceParallelProof.halves_equal: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend as ReduceParallelProof
Lines 700-712 of bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend&start_line=700&end_line=712

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce

# A split hands each half the contribution array.
def halves_equal(+d: Nat, -A: Array<F32>, pair: Array<F32> & Array<F32>, -exact: {pair == Array.clone(F32, A) : Array<F32> & Array<F32>},
  -valid: Model.Balanced(F32, d, A)) ->
  Parallel.Fact<({Pair.fst(Array<F32> & Unit, Array<F32> & Unit, Reduce.halves(pair)) == (A, Unit{}) : Array<F32> & Unit} &
    {Pair.snd(Array<F32> & Unit, Array<F32> & Unit, Reduce.halves(pair)) == (A, Unit{}) : Array<F32> & Unit})>:
  (first, second) = pair
  Parallel.Fact{(
    Equal.cong(Array<F32>, Array<F32> & Unit, a => (a, Unit{}), first, A,
      {\{Parallel.Fact: p => p} : Parallel.Fact<({Pair.fst(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>})> ->
        {Pair.fst(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>}}(Parallel.clone_first(d, A, A, (first, second), exact, {==}, valid))),
    Equal.cong(Array<F32>, Array<F32> & Unit, a => (a, Unit{}), second, A,
      {\{Parallel.Fact: p => p} : Parallel.Fact<({Pair.snd(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>})> ->
        {Pair.snd(Array<F32>, Array<F32>, (first, second)) == A : Array<F32>}}(Parallel.clone_second(d, A, A, (first, second), exact, {==}, valid))))}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.clone
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.fst
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=halves
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Balanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=Fact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=clone_first
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=clone_second