PROOF.run_go_le: def of bend-osdev-acpi@0.1.1.0
Import: import bend-osdev-acpi@0.1.1.0/PROOF.bend as PROOF
Lines 2522-2532 of bend-osdev-acpi@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-acpi@0.1.1.0/PROOF.bend&start_line=2522&end_line=2532

import Base
import bend-osdev-acpi@0.1.1.0/aml_host.bend as Hs
import bend-osdev-acpi@0.1.1.0/aml_interp.bend as I
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def run_go_le(+n: Nat, +h: Bool, +m: I.AmlMachine<Hs.AmlMemHost>, +u: Nat) -> {Nat.is_le(I.AmlRun.steps(Hs.AmlMemHost, I.AmlM.run.go(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, n, h, m, u)), Nat.add(n, u)) == True{} : Bool}:
  match n:
    case 0n:
      UL.nat_le_refl(u)
    case 1n+p:
      match h:
        case True{}:
          le_step(u, Nat.add(p, u), UL.nat_le_add(u, p))
        case False{}:
          %Equal.sym(Nat, 1n+Nat.add(p, u), Nat.add(p, 1n+u), add_succ(p, u)) : {Nat.is_le(I.AmlRun.steps(Hs.AmlMemHost, I.AmlM.run.go(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, p, I.AmlMachine.halted(Hs.AmlMemHost, I.AmlM.step(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, m)), I.AmlM.step(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, m), 1n+u)), _) == True{} : Bool}
          run_go_le(p, I.AmlMachine.halted(Hs.AmlMemHost, I.AmlM.step(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, m)), I.AmlM.step(~Hs.AmlMemHost, ~Hs.AmlMemHost.io, m), 1n+u)

Uses (16):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/PROOF.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/PROOF.bend&name=le_step
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_host.bend&name=AmlMemHost
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_host.bend&name=AmlMemHost.io
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_interp.bend&name=AmlM.run.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_interp.bend&name=AmlM.step
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_interp.bend&name=AmlMachine
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_interp.bend&name=AmlMachine.halted
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.1.0/aml_interp.bend&name=AmlRun.steps
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_add
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_le_refl