BackwardPROOF.not_lt_succ_lt: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 68-76 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=68&end_line=76

import Base

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

Uses (5):
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=true_false