BackwardPROOF.operands_bounded: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 437-452 of bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&start_line=437&end_line=452

import Base
import bendtorch-core@0.1.0.0/src/autograd/backward.bend as Backward
import bendtorch-core@0.1.0.0/src/autograd/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}:
      Equal.cong(Bool, Bool, flag => Bool.and(Nat.is_lt(a, bound), flag), Nat.is_lt(b, bound), Bool.and(Nat.is_lt(b, bound), True{}),
        Equal.sym(Bool, Bool.and(Nat.is_lt(b, bound), True{}), Nat.is_lt(b, bound), and_true(Nat.is_lt(b, bound))))
    case Backward.Sub{a, b}:
      Equal.cong(Bool, Bool, flag => Bool.and(Nat.is_lt(a, bound), flag), Nat.is_lt(b, bound), Bool.and(Nat.is_lt(b, bound), True{}),
        Equal.sym(Bool, Bool.and(Nat.is_lt(b, bound), True{}), Nat.is_lt(b, bound), and_true(Nat.is_lt(b, bound))))
    case Backward.Mul{a, b, left, right}:
      Equal.cong(Bool, Bool, flag => Bool.and(Nat.is_lt(a, bound), flag), Nat.is_lt(b, bound), Bool.and(Nat.is_lt(b, bound), True{}),
        Equal.sym(Bool, Bool.and(Nat.is_lt(b, bound), True{}), Nat.is_lt(b, bound), and_true(Nat.is_lt(b, bound))))
    case Backward.Neg{a}:
      Equal.sym(Bool, Bool.and(Nat.is_lt(a, bound), True{}), Nat.is_lt(a, bound), and_true(Nat.is_lt(a, 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.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=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/backward.bend&name=Node
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=operands_below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=targets
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=and_true