ReduceReplayedProof.above_false: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend as ReduceReplayedProof
Lines 160-170 of bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&start_line=160&end_line=170

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

# k < b gives b < 1 + k false.
def above_false(+k: Nat, +b: Nat, h: {Nat.is_lt(k, b) == True{} : Bool}) -> {Nat.is_lt(b, 1n+k) == False{} : Bool}:
  match k b:
    case 0n 0n:
      Empty.absurd({Nat.is_lt(0n, 1n) == False{} : Bool}, Arith.clash(h))
    case 0n 1n+q:
      lt_zero_false(q)
    case 1n+p 0n:
      Empty.absurd({Nat.is_lt(0n, 1n+(1n+p)) == False{} : Bool}, Arith.clash(h))
    case 1n+p 1n+q:
      above_false(p, q, h)

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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_replayed_proof.bend&name=lt_zero_false
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash