CorePROOF.prefix_previous: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend as CorePROOF
Lines 757-783 of bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&start_line=757&end_line=783

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
import bendtorch-core@0.1.0.0/src/tensor/elementwise.bend as Elementwise

def prefix_previous(+operation: Elementwise.Operation, +plan: Shape.BroadcastPlan,
  -original_left: Core.Dynamic, -original_right: Core.Dynamic, +cursor: Nat, +index: U32,
  -before: Core.Tensor<Shape.output_shape(plan)>, -after: Core.Tensor<Shape.output_shape(plan)>,
  converted: {U32.to_nat(index) == cursor : Nat},
  prefix: Elementwise.PrefixInvariant(operation, plan, original_left, original_right, cursor, Core.Packed{Shape.output_shape(plan), before}),
  frame: @+other: U32 -> @checked: Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), before}, other) ->
    @different: {Nat.is_eq(U32.to_nat(index), U32.to_nat(other)) == False{} : Bool} ->
      Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), after}, other) &
        {Core.observe(Shape.output_shape(plan), after, other) == Core.observe(Shape.output_shape(plan), before, other) : Maybe<&2, F32>},
  +other: U32, +earlier: Shape.LT(U32.to_nat(other), cursor)) ->
  Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), after}, other) &
    {Core.observe(Shape.output_shape(plan), after, other) == Elementwise.expected(operation, plan, original_left, original_right, other) : Maybe<&2, F32>}:
  {\{Tuple: before_checked => before_equal =>
    {\{Tuple: after_checked => after_equal => (after_checked,
      Equal.trans(Maybe<&2, F32>, Core.observe(Shape.output_shape(plan), after, other), Core.observe(Shape.output_shape(plan), before, other),
        Elementwise.expected(operation, plan, original_left, original_right, other), after_equal, before_equal))} :
      (Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), after}, other) &
        {Core.observe(Shape.output_shape(plan), after, other) == Core.observe(Shape.output_shape(plan), before, other) : Maybe<&2, F32>}) ->
      (Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), after}, other) &
        {Core.observe(Shape.output_shape(plan), after, other) == Elementwise.expected(operation, plan, original_left, original_right, other) : Maybe<&2, F32>})}(frame(other)(before_checked)(
          %Equal.sym(Nat, U32.to_nat(index), cursor, converted) : {Nat.is_eq(_, U32.to_nat(other)) == False{} : Bool}
          lt_big_small_different(U32.to_nat(other), cursor, earlier)))
  } :
    (Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), before}, other) &
      {Core.observe(Shape.output_shape(plan), before, other) == Elementwise.expected(operation, plan, original_left, original_right, other) : Maybe<&2, F32>}) ->
    (Core.ObservationChecked(Core.Packed{Shape.output_shape(plan), after}, other) &
      {Core.observe(Shape.output_shape(plan), after, other) == Elementwise.expected(operation, plan, original_left, original_right, other) : Maybe<&2, F32>})}(prefix(other)(earlier))

Uses (22):
  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=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=Nat.is_eq
  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=BroadcastPlan
  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=output_shape
  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=observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&name=lt_big_small_different
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=Operation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=PrefixInvariant
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=expected