NatOrder.lt_succ: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 305-315 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=305&end_line=315

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

# Order structure shared by padding, allocation and mixed-radix indexing.
def lt_succ(+a: Nat,+b: Nat,h: {Nat.is_le(a,b) == True{} : Bool}) -> {Nat.is_lt(a,1n+b) == True{} : Bool}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+b:
      {==}
    case 1n+a 0n:
      Empty.absurd({Nat.is_lt(1n+a,1n) == True{} : Bool},WordEncoding.false_true(h))
    case 1n+a 1n+b:
      lt_succ(a,b,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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true