ProjectionProofs.dot_broadcast: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend as ProjectionProofs
Lines 105-113 of bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend&start_line=105&end_line=113

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

def dot_broadcast(+dims: List<&2, Nat>, +values: List<&2, Nat>) -> {dot(strides_of(dims), values) == Shape.offset(dims, Shape.broadcast_indices(dims, values)) : Nat}:
  match dims values:
    case +head <> +tail +value <> +rest:
      %Equal.sym(Nat, dot(strides_of(tail), rest), Shape.offset(tail, Shape.broadcast_indices(tail, rest)), dot_broadcast(tail, rest)) : {Nat.add(Nat.mul(Shape.broadcast_index(head, Shape.numel(tail)), value), _) == Nat.add(Nat.mul(Shape.broadcast_index(head, value), Shape.numel(tail)), Shape.offset(tail, Shape.broadcast_indices(tail, rest))) : Nat}
      Equal.cong(Nat, Nat, term => Nat.add(term, Shape.offset(tail, Shape.broadcast_indices(tail, rest))), Nat.mul(Shape.broadcast_index(head, Shape.numel(tail)), value), Nat.mul(Shape.broadcast_index(head, value), Shape.numel(tail)), axis_term(head, Shape.numel(tail), value))
    case Nil{} values:
      {==}
    case head <> tail Nil{}:
      {==}

Uses (13):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=broadcast_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=broadcast_indices
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=offset
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend&name=axis_term
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend&name=dot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend&name=strides_of