ReduceFiberProof.gt_not_eq: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 322-329 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=322&end_line=329

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

def gt_not_eq(+a: Nat, +b: Nat, h: {Nat.is_lt(b, a) == True{} : Bool}) -> {Nat.is_eq(a, b) == False{} : Bool}:
  match a b:
    case 0n b:
      Empty.absurd({Nat.is_eq(0n, b) == False{} : Bool}, Arith.lt_zero(b, h))
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      gt_not_eq(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_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/storage/arith.bend&name=lt_zero