NatOrder.below_difference: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 357-366 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=357&end_line=366

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

# Translate a comparison against a remaining extent to its absolute position.
def below_difference(+offset: Nat,+value: Nat,+end: Nat,ordered: {Nat.is_le(offset,end) == True{} : Bool}) ->
  {Nat.is_lt(value,Nat.sub(end,offset)) == Nat.is_lt(Nat.add(offset,value),end) : Bool}:
  match offset end:
    case 0n end:
      %Equal.sym(Nat,Nat.sub(end,0n),end,subtract_zero(end)) : {Nat.is_lt(value,_) == Nat.is_lt(value,end) : Bool}
      {==}
    case 1n+offset 0n:
      Empty.absurd({Nat.is_lt(value,Nat.sub(0n,1n+offset)) == Nat.is_lt(Nat.add(1n+offset,value),0n) : Bool},WordEncoding.false_true(ordered))
    case 1n+offset 1n+end: below_difference(offset,value,end,ordered)

Uses (10):
  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.add
  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=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=subtract_zero
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true