PointwiseProof.writes_value: 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 216-237 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=216&end_line=237

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/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend as Pointwise

def writes_value(~O: Data, ~f: O -> F32 -> F32 -> F32, ~P: Data, ~ia: P -> Nat -> Nat, ~ib: P -> Nat -> Nat,
  +count: Nat, +operation: O, +plan: P, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>,
  +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +shape: Shape.Shape, +index: U32,
  below: {Nat.is_lt(U32.to_nat(index), count) == True{} : Bool},
  +room: {Nat.is_le(count, Shape.logical_numel(Shape.dimensions(shape))) == True{} : Bool}) ->
  {Replayed.value(shape, 0.0, Pointwise.writes(~O, ~f, ~P, ~ia, ~ib, count, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), index) ==
    Pointwise.cell(~O, ~f, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(index)) : F32}:
  match count:
    case 0n:
      Empty.absurd({Replayed.value(shape, 0.0, Nil{}, index) ==
        Pointwise.cell(~O, ~f, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(index)) : F32},
        Arith.lt_zero(U32.to_nat(index), below))
    case 1n+previous:
      write_split(shape, Pointwise.writes(~O, ~f, ~P, ~ia, ~ib, previous, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops),
        previous, Pointwise.cell(~O, ~f, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous), index,
        Pointwise.cell(~O, ~f, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(index)),
        below, room,
        at => Equal.cong(Nat, F32, position => Pointwise.cell(~O, ~f, ~P, ~ia, ~ib, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, position),
          previous, U32.to_nat(index), Equal.sym(Nat, U32.to_nat(index), previous, at)),
        earlier => writes_value(~O, ~f, ~P, ~ia, ~ib, previous, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops,
          shape, index, earlier, Conversion.le_predecessor(previous, Shape.logical_numel(Shape.dimensions(shape)), room)),
        Shape.bool_case(Nat.is_eq(U32.to_nat(index), previous)))

Uses (23):
  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=Equal.cong
  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.is_eq
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  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=bool_case
  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/arith.bend&name=lt_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=writes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=write_split
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_predecessor