TensorBackwardPROOF.frozen_nt_spared: 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 195-205 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=195&end_line=205

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

def frozen_nt_spared(+id: Nat, +a: Nat, +b: Nat, +left: Shape.Shape, +right: Shape.Shape, saved: Backward.Saved, g: Core.Dynamic,
  decision: Shape.BoolCase<Bool.and(Nat.is_eq(id, a), Bool.not(Nat.is_eq(id, b)))>) ->
  {Laws.sends_to(id, Backward.nt_frozen(id, a, b, left, right, saved, g, Bool.and(Nat.is_eq(id, a), Bool.not(Nat.is_eq(id, b))))) == False{} : Bool}:
  match decision:
    case Shape.BTrue{+equal}:
      %equal : {Laws.sends_to(id, Backward.nt_frozen(id, a, b, left, right, saved, g, _)) == False{} : Bool}
      right_alone_spared(id, b, right, saved, g,
        other_operand(Nat.is_eq(id, a), Nat.is_eq(id, b), Equal.sym(Bool, True{}, Bool.and(Nat.is_eq(id, a), Bool.not(Nat.is_eq(id, b))), equal)))
    case Shape.BFalse{equal}:
      %equal : {Laws.sends_to(id, Backward.nt_frozen(id, a, b, left, right, saved, g, _)) == False{} : Bool}
      unsent_spared(id, Backward.vjp_matmul_nt(a, b, left, right, saved, g))

Uses (16):
  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=Bool.not
  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_eq
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Saved
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=nt_frozen
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=vjp_matmul_nt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend&name=sends_to
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&name=other_operand
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&name=right_alone_spared
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&name=unsent_spared
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BoolCase
  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/core.bend&name=Dynamic