ReduceReplayedProof.leaf_eq: 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 451-461 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=451&end_line=461

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_storage_proof.bend as Owned
import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_build_proof.bend as Build
import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as Par
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce

def leaf_eq(+base: Nat, +accumulator: F32, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>,
  +h: List<&2, Api.Effect>, +d: Nat, +f: F32, +source: Par.Source<shape, fill, ops, h, d, f>,
  +below: {Nat.is_lt(base, Shape.logical_numel(Shape.dimensions(shape))) == True{} : Bool},
  pair: Array<F32> & F32, +exact: {pair == Array.get(F32, Api.arr(h, d, f), U32.from_nat(base)) : Array<F32> & F32}) ->
  {Reduce.leaf_add(accumulator, pair) == (rfold(shape, fill, ops, [base], accumulator), Api.arr(h, d, f)) : F32 & Array<F32>}:
  (kept, word) = pair
  Owned.pair_eq(F32, Array<F32>, F32.add(accumulator, word), F32.add(accumulator, Replayed.value(shape, fill, ops, U32.from_nat(base))),
    kept, Api.arr(h, d, f),
    Equal.cong(F32, F32, w => F32.add(accumulator, w), word, Replayed.value(shape, fill, ops, U32.from_nat(base)),
      Par.source_read(shape, fill, ops, h, d, f, source, U32.from_nat(base), Par.index_inside(shape, base, below), (kept, word), exact)),
    Build.got_kept(d, h, f, U32.from_nat(base), (kept, word), exact))

Uses (26):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=F32.add
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=leaf_add
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=rfold
  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/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=logical_numel
  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=Effect
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/api.bend&name=arr
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_build_proof.bend&name=got_kept
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_storage_proof.bend&name=pair_eq
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=Source
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=index_inside
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=source_read
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value