SlicePROOF.lt_succ_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 141-148 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=141&end_line=148

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

def lt_succ_le(+k: Nat, +q: Nat, h: {Nat.is_lt(k, 1n+q) == True{} : Bool}) -> {Nat.is_le(k, q) == True{} : Bool}:
  match k q:
    case 0n _:
      Arith.le_zero(q)
    case 1n+p 0n:
      Empty.absurd({Nat.is_le(1n+p, 0n) == True{} : Bool}, Arith.lt_zero(p, h))
    case 1n+p 1n+r:
      lt_succ_le(p, r, h)

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.is_lt
  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/storage/arith.bend&name=lt_zero