BackwardPROOF.not_lt_succ_ne: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 58-66 of bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&start_line=58&end_line=66

import Base

def not_lt_succ_ne(+id: Nat, +bound: Nat, outside: {Nat.is_lt(id, 1n+bound) == False{} : Bool}) ->
  {False{} == Nat.is_eq(bound, id) : Bool}:
  match id bound:
    case 0n bound:
      Empty.absurd({False{} == Nat.is_eq(bound, 0n) : Bool}, true_false(outside))
    case 1n+rest 0n:
      {==}
    case 1n+rest 1n+smaller:
      not_lt_succ_ne(rest, smaller, outside)

Uses (6):
  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_eq
  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/autograd/backward_PROOF.bend&name=true_false