IndexProofs.left_value: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as IndexProofs
Lines 51-61 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=51&end_line=61

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

def left_value(+a: Nat, +b: Nat, +index: Shape.Fin(a)) -> {Shape.Fin.value(Nat.add(a, b), Shape.Fin.left(a, b, index)) == Shape.Fin.value(a, index) : Nat}:
  match a:
    case 0n:
      match index:
    case 1n+p:
      match index:
        case Shape.FZero{}:
          {==}
        case Shape.FNext{+previous}:
          %left_value(p, b, previous) : {1n+Shape.Fin.value(Nat.add(p, b), Shape.Fin.left(p, b, previous)) == 1n+_ : Nat}
          {==}

Uses (6):
  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.left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.value