ReduceFiberProof.shift_append: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 565-572 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=565&end_line=572

import Base

def shift_append(+base: Nat, +xs: List<&2, Nat>, +ys: List<&2, Nat>) ->
  {shift(base, List.append(&2, Nat, xs, ys)) == List.append(&2, Nat, shift(base, xs), shift(base, ys)) : List<&2, Nat>}:
  match xs:
    case Nil{}:
      {==}
    case +x <> +rest:
      Equal.cong(List<&2, Nat>, List<&2, Nat>, tail => Nat.add(base, x) <> tail,
        shift(base, List.append(&2, Nat, rest, ys)), List.append(&2, Nat, shift(base, rest), shift(base, ys)), shift_append(base, rest, ys))

Uses (6):
  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=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&name=shift