TransformPROOF.earlier_split: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 281-292 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=281&end_line=292

import Base

def earlier_split(+a: Nat, +b: Nat, earlier: {Nat.is_lt(a, 1n+b) == True{} : Bool}) ->
  Either<&2, &2, {Nat.is_lt(a, b) == True{} : Bool}, {a == b : Nat}>:
  match a b:
    case 0n 0n:
      Inr{{==}}
    case 0n 1n+q:
      Inl{{==}}
    case 1n+p 0n:
      Empty.absurd(Either<&2, &2, {Nat.is_lt(1n+p, 0n) == True{} : Bool}, {1n+p == 0n : Nat}>,
        earlier_zero_false(p, earlier))
    case 1n+p 1n+q:
      earlier_lift(p, q, earlier_split(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=Either
  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/tensor/transform_PROOF.bend&name=earlier_lift
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=earlier_zero_false