ProofBsearch.bq.lt_le: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/proof_bsearch.bend as ProofBsearch
Lines 170-177 of bend-osdev-algo@0.1.0.0/proof_bsearch.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&start_line=170&end_line=177

import Base

def bq.lt_le(x: Nat, y: Nat, h: {Nat.is_lt(x, y) == True{} : Bool}) -> {Nat.is_le(x, y) == True{} : Bool}:
  match x y:
    case 0n _:
      bq.le_zero(y)
    case 1n+xp 0n:
      Empty.absurd({Nat.is_le(1n+xp, 0n) == True{} : Bool}, bq.ft(h))
    case 1n+xp 1n+yp:
      bq.lt_le(xp, yp, h)

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=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=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.ft
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.le_zero