PROOF.bitseq.next_le: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 573-594 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=573&end_line=594

import Base
import bend-osdev-algo@0.1.0.0/bitmap.bend as M

def bitseq.next_le(size: Nat, start: Nat, want: Bool, bs: List<&2, Bool>) -> {Nat.is_le(M.bitseq.next(size, start, want, bs), size) == True{} : Bool}:
  match size:
    case 0n:
      {==}
    case 1n+ +s:
      match start want bs:
        case 1n+st w Nil{}:
          bitseq.next_le(s, st, w, Nil{})
        case 1n+st w Con{h, t}:
          bitseq.next_le(s, st, w, t)
        case 0n False{} Nil{}:
          {==}
        case 0n True{} Nil{}:
          nat.le_refl(s)
        case 0n True{} Con{True{}, t}:
          {==}
        case 0n False{} Con{False{}, t}:
          {==}
        case 0n True{} Con{False{}, t}:
          bitseq.next_le(s, 0n, True{}, t)
        case 0n False{} Con{True{}, t}:
          bitseq.next_le(s, 0n, False{}, t)

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=List
  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=bend-osdev-algo@0.1.0.0/PROOF.bend&name=nat.le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bitmap.bend&name=bitseq.next