TensorBackwardPROOF.operands_bounded: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend as TensorBackwardPROOF
Lines 296-330 of bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&start_line=296&end_line=330

import Base
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend as Backward
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend as Laws

def operands_bounded(+node: Backward.Node, +bound: Nat) ->
  {Backward.operands_below(node, bound) == Laws.bounded(Laws.targets(node), bound) : Bool}:
  match node:
    case Backward.Leaf{}:
      {==}
    case Backward.Add{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.Sub{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.Mul{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.Sum{a, input}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.SumDims{a, input, kept}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.Matmul{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.MatmulNT{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.Relu{a, input}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.MseLoss{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.CrossEntropy{a, input}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.BatchedMatmul{a, b, left, right}:
      pair_bounded(a, b, bound)
    case Backward.Slice{a, input, kept, plan}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.Gathered{a, input, plan, entries}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, bound)))
    case Backward.Constant{}:
      {==}
    case Backward.Frozen{id, inner}:
      operands_bounded(inner, bound)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Node
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=operands_below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend&name=targets
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&name=and_true
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&name=pair_bounded