NatOrder.not_below: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 8-13 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=8&end_line=13

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

def not_below(+lower: Nat,+value: Nat,room: {Nat.is_le(lower,value) == True{} : Bool}) -> {Nat.is_lt(value,lower) == False{} : Bool}:
  match lower value:
    case 0n 0n: {==}
    case 0n 1n+value: {==}
    case 1n+lower 0n: Empty.absurd({True{} == False{} : Bool},WordEncoding.false_true(room))
    case 1n+lower 1n+value: not_below(lower,value,room)

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