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Proof step 35 from proof refine-fsync (previous step)

# links(m, cache_dirs) = m4, cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs1 = cache_dirs, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∀ cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced, err. afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache → cache_dirs = dirs1 → err = ESUCCESS ∨ ⌊err⌋ → icache-cons(cache_icache, dirs1, cache_files) ∧ dcache-cons(cache_dcache, dirs1, cache_files) ∧ pcache-cons(cache_pcache, dirs1, cache_files) ∧ synced(dirs1, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(dirs1, cache_files) → ⟨afs_fsync#(mkinode(m, md, false, m4, 0, m2), asynced, dirs1, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err0)⟩ ((afs_asynced ↔ cache_asynced) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, cache_files0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache0, cache_pcache0), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨afs_fsync# (mkinode(m, md, false, # links(m, cache_dirs), 0, m2), asynced, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err0)⟩ ((afs_asynced ↔ cache_asynced) ∧ err = err0)

Proof step 35 from proof refine-fsync (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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