SlicePROOF.sub_zero_le: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 131-139 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=131&end_line=139

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith

# stop - low = 0 gives stop <= low.
def sub_zero_le(+stop: Nat, +low: Nat, e: {Nat.sub(stop, low) == 0n : Nat}) -> {Nat.is_le(stop, low) == True{} : Bool}:
  match stop low:
    case 0n _:
      Arith.le_zero(low)
    case 1n+ap 0n:
      Empty.absurd({Nat.is_le(1n+ap, 0n) == True{} : Bool}, nat_clash(ap, e))
    case 1n+ap 1n+lp:
      sub_zero_le(ap, lp, e)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=le_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&name=nat_clash