ReduceReplayedProof.above: 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 291-308 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=291&end_line=308

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api

# A subtree whose positions all lie above k is the same for k and 1 + k.
def above(+plan: Shape.BroadcastPlan, +map: PlanMap(plan), +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +k: Nat, +depth: Nat, +b: Nat, +h: {Nat.is_lt(k, b) == True{} : Bool}) ->
  {out_spec(plan, map, shape, fill, ops, k, depth, b) == out_spec(plan, map, shape, fill, ops, 1n+k, depth, b) : Array<F32>}:
  match depth:
    case 0n:
      %Equal.sym(Bool, Nat.is_lt(b, k), False{}, lt_asym(k, b, h)) :
        {ALeaf{out_leaf(plan, map, shape, fill, ops, b, _)} == ALeaf{out_leaf(plan, map, shape, fill, ops, b, Nat.is_lt(b, 1n+k))} : Array<F32>}
      %Equal.sym(Bool, Nat.is_lt(b, 1n+k), False{}, above_false(k, b, h)) :
        {ALeaf{0.0} == ALeaf{out_leaf(plan, map, shape, fill, ops, b, _)} : Array<F32>}
      {==}
    case 1n+inner:
      +high = Nat.add(Model.capacity(inner), b)
      %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, b), out_spec(plan, map, shape, fill, ops, 1n+k, inner, b), above(plan, map, shape, fill, ops, k, inner, b, h)) :
        {ANode{_, out_spec(plan, map, shape, fill, ops, k, inner, high)} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
      %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, high), out_spec(plan, map, shape, fill, ops, 1n+k, inner, high),
        above(plan, map, shape, fill, ops, k, inner, high, Arith.lt_le_trans(k, b, high, h, Api.le_add_left(Model.capacity(inner), b)))) :
        {ANode{out_spec(plan, map, shape, fill, ops, 1n+k, inner, b), _} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
      {==}

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  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=F32
  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.add
  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_replayed_proof.bend&name=PlanMap
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=above_false
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=lt_asym
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=out_leaf
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=out_spec
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/api.bend&name=le_add_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=capacity