TransformPROOF.natural_lt_different: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 700-710 of bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&start_line=700&end_line=710

import Base
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle

def natural_lt_different(+a: Nat, +b: Nat, earlier: {Nat.is_lt(a, b) == True{} : Bool}) ->
  {Nat.is_eq(b, a) == False{} : Bool}:
  match a b:
    case 0n 0n:
      Empty.absurd({True{} == False{} : Bool}, Lifecycle.false_true(Equal.sym(Bool, False{}, True{}, earlier)))
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      {==}
    case 1n+p 1n+q:
      natural_lt_different(p, q, earlier)

Uses (7):
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=false_true