ReduceFiberProof.le_ne_succ: 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 331-341 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=331&end_line=341

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

def le_ne_succ(+a: Nat, +b: Nat, le: {Nat.is_le(a, b) == True{} : Bool}, ne: {Nat.is_eq(a, b) == False{} : Bool}) ->
  {Nat.is_le(1n+a, b) == True{} : Bool}:
  match a b:
    case 0n 0n:
      Empty.absurd({Nat.is_le(1n, 0n) == True{} : Bool}, Arith.clash(Equal.sym(Bool, Nat.is_eq(0n, 0n), False{}, ne)))
    case 0n 1n+q:
      Arith.le_zero(q)
    case 1n+p 0n:
      Empty.absurd({Nat.is_le(2n+p, 0n) == True{} : Bool}, Arith.clash(le))
    case 1n+p 1n+q:
      le_ne_succ(p, q, le, ne)

Uses (8):
  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=Equal.sym
  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_le
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=le_zero