IndexProofs.merge_split: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as IndexProofs
Lines 39-49 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=39&end_line=49

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

def merge_split(+a: Nat, +b: Nat, +index: Shape.Fin(Nat.add(a, b))) -> {Shape.Fin.merge(a, b, Shape.Fin.split(a, b, index)) == index : Shape.Fin(Nat.add(a, b))}:
  match a:
    case 0n:
      {==}
    case 1n+p:
      match index:
        case Shape.FZero{}:
          {==}
        case Shape.FNext{+previous}:
          %merge_split(p, b, previous) : {Shape.Fin.merge(1n+p, b, Shape.Fin.split.step(p, b, Shape.Fin.split(p, b, previous))) == Shape.FNext{_} : Shape.Fin(1n+Nat.add(p, b))}
          merge_step(p, b, Shape.Fin.split(p, b, previous))

Uses (8):
  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/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.merge
  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
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/index_proofs.bend&name=merge_step