IndexProofs.split_left: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as IndexProofs
Lines 12-22 of bendtorch-core@0.1.0.0/src/shape/index_proofs.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/shape/index_proofs.bend&start_line=12&end_line=22

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

def split_left(+a: Nat, +b: Nat, +index: Shape.Fin(a)) -> {Shape.Fin.split(a, b, Shape.Fin.left(a, b, index)) == Inl{index} : Either<Shape.Fin(a), Shape.Fin(b)>}:
  match a:
    case 0n:
      match index:
    case 1n+p:
      match index:
        case Shape.FZero{}:
          {==}
        case Shape.FNext{+previous}:
          %split_left(p, b, previous) : {Shape.Fin.split.step(p, b, Shape.Fin.split(p, b, Shape.Fin.left(p, b, previous))) == Shape.Fin.split.step(p, b, _) : Either<Shape.Fin(1n+p), Shape.Fin(b)>}
          {==}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Either
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.Step
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.split
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.split.step