U32.internal_succ_double_lt: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 6-15 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=6&end_line=15

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

def internal_succ_double_lt(a: Nat, b: Nat, h: MNat.lt(a, b)) -> MNat.lt(1n+Nat.double(a), Nat.double(b)):
  match a b:
    case 0n 0n:
      Empty.absurd(MNat.lt(1n, 0n), MNat.internal_false_ne_true(h))
    case 0n 1n+q:
      {==}
    case 1n+p 0n:
      Empty.absurd(MNat.lt(3n+Nat.double(p), 0n), MNat.internal_false_ne_true(h))
    case 1n+p 1n+q:
      internal_succ_double_lt(p, q, h)

Uses (5):
  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.double
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_false_ne_true
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt