ProofBsearch.bq.sub_step: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/proof_bsearch.bend as ProofBsearch
Lines 327-335 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=327&end_line=335

import Base

def bq.sub_step(q: Nat, k: Nat) -> {Nat.is_le(Nat.sub(q, k), 1n+Nat.sub(q, 1n+k)) == True{} : Bool}:
  match q k:
    case 0n _:
      {==}
    case 1n+ +qp 0n:
      %Equal.sym(Nat, Nat.sub(qp, 0n), qp, bq.sub_zero(qp)) : {Nat.is_le(1n+qp, 1n+_) == True{} : Bool}
      bq.le_refl(qp)
    case 1n+qp 1n+kp:
      bq.sub_step(qp, kp)

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=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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/proof_bsearch.bend&name=bq.sub_zero