BatchedMatmulPROOF.naturals_append: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedMatmulPROOF
Lines 655-662 of bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&start_line=655&end_line=662

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

def naturals_append(+xs: List<&2, U32>, +ys: List<&2, U32>) ->
  {Shape.naturals(List.append(&2, U32, xs, ys)) == List.append(&2, Nat, Shape.naturals(xs), Shape.naturals(ys)) : List<&2, Nat>}:
  match xs:
    case Nil{}:
      {==}
    case +head <> tail:
      Equal.cong(List<&2, Nat>, List<&2, Nat>, rest => U32.to_nat(head) <> rest,
        Shape.naturals(List.append(&2, U32, tail, ys)), List.append(&2, Nat, Shape.naturals(tail), Shape.naturals(ys)), naturals_append(tail, ys))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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=naturals