ConstructionPROOF.fill_head: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/construction_PROOF.bend as ConstructionPROOF
Lines 219-240 of bendtorch-core@0.1.0.0/src/tensor/construction_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/construction_PROOF.bend&start_line=219&end_line=240

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core

def fill_head(-shape: Shape.Shape, -written: Core.Tensor<shape>, -tensor: Core.Tensor<shape>, +cursor: Nat, +value: F32,
  point: @+index: U32 -> @at: {U32.to_nat(index) == cursor : Nat} ->
    Core.ObservationChecked(Core.Packed{shape, written}, index) &
      {Core.checked_observe(shape, written, index) == Some{value} : Maybe<&2, F32>},
  frame: FillFrame(shape, written, 1n+cursor, tensor), +index: U32, +at: {U32.to_nat(index) == cursor : Nat}) ->
  Core.ObservationChecked(Core.Packed{shape, tensor}, index) &
    {Core.checked_observe(shape, tensor, index) == Some{value} : Maybe<&2, F32>}:
  {\{Tuple: checked => observed =>
    {\{Tuple: after_checked => retained =>
      (after_checked, Equal.trans(Maybe<&2, F32>, Core.checked_observe(shape, tensor, index), Core.checked_observe(shape, written, index),
        Some{value}, retained, observed))} :
      (Core.ObservationChecked(Core.Packed{shape, tensor}, index) &
        {Core.checked_observe(shape, tensor, index) == Core.checked_observe(shape, written, index) : Maybe<&2, F32>}) ->
      (Core.ObservationChecked(Core.Packed{shape, tensor}, index) &
        {Core.checked_observe(shape, tensor, index) == Some{value} : Maybe<&2, F32>})}(frame(index)(
          %Equal.sym(Nat, U32.to_nat(index), cursor, at) : Shape.LT(_, 1n+cursor)
          lt_self_successor(cursor))(checked))
  } :
    (Core.ObservationChecked(Core.Packed{shape, written}, index) &
      {Core.checked_observe(shape, written, index) == Some{value} : Maybe<&2, F32>}) ->
    (Core.ObservationChecked(Core.Packed{shape, tensor}, index) &
      {Core.checked_observe(shape, tensor, index) == Some{value} : Maybe<&2, F32>})}(point(index)(at))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=Sigma
  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=LT
  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/tensor/construction_PROOF.bend&name=FillFrame
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/construction_PROOF.bend&name=lt_self_successor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=ObservationChecked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=checked_observe