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Proof step 7 from proof refine-fsync (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)⟫ ⟨afs_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 8:
icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), afs-cons(dirs, files), valid-file-inode(inode, dirs, files) ⊦ ⟪cache_fsync#(inode, asynced0, asynced; dirs, files, icache, pcache, asynced1; err)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))
Proof step 9:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), 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) ⊦ icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) ∧ valid-file-inode(mkinode(m, md, false, m1, 0, m2), cache_dirs, cache_files)
Proof step 22:
asynced2 ↔ cache_sync, asynced3 ↔ asynced, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dcache0 = cache_dcache, inode0 = mkinode(m, md, false, m1, 0, m2), 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), valid-file-inode(mkinode(m, md, false, m1, 0, m2), cache_dirs, cache_files), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ [cache_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(dcache0, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (asynced2 → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨afs_fsync#(mkinode(m, md, false, m1, 0, m2), asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0))

Rule argument

spec: cache-asm name: inv-fsync seq: icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), afs-cons(dirs, files), valid-file-inode(inode, dirs, files) ⊦ ⟪cache_fsync# (inode, asynced0, asynced ; dirs, files, icache, pcache, asynced1 ; err)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files)) subst: [asynced, asynced0, inode, asynced1, pcache, icache, files, dirs, err, dcache] → [cache_sync, asynced, mkinode(m, md, false, m1, 0, m2), cache_asynced, cache_pcache, cache_icache, cache_files, cache_dirs, err, cache_dcache] flags: List([[1,0,0]])

Proof step 7 from proof refine-fsync (previous step)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

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