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Proof step 110 from proof refine-rmdir (previous step)

(m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs), m1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m6 ⊃ mkdir(m0, md1, # links(entries0[str], cache_dirs), m1, entries0 -- str) ;mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), cache_dirs[m6] = mkdir(m0 + 1, md1, # links(m6, cache_dirs), m1 + 1, entries0), cache_dirs[entries0[str]] = mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅), cache_dirs2 = cache_dirs, cache_dirs3 = cache_dirs, dcache = cache_dcache, dent0 = mkdentry(str, entries0[str]), err = ESUCCESS, key = dentrykey(p_ino, name), name = str, p_ino = m6, p_inode0 = mkinode(m6, md, true, # links(m6, cache_dirs), m1 + 1, m0 + 1), p_inode1 = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons (cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (dcache -- key, cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_pcache), entries0[str] ∈ cache_dirs, m6 ∈ cache_dirs, str ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ ⟨afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_rmdir#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2 [m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m6, cache_dirs2), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m6 ∧ entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md, m3, m7, entries) ;(entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md2, m3, m7, entries);cache_dirs2[entries0[str]]) ) .meta:= md0 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ] ∧ (afs_asynced ↔ asynced0) ∧ (m6 ∈ cache_dirs2 ⊃ mkinode (m6, (m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs2), m1, entries0 -- str)).meta, true, (m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs2), m1, entries0 -- str)).nlink, (m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs2), m1, entries0 -- str)).nsubdirs, (m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs2), m1, entries0 -- str)).size) ;mkinode(m6, cache_files[m6].meta, false, cache_files[m6].nlink, 0, cache_files[m6].size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs3 ⊃ mkinode(entries0[str], md0, true, m8, m9, m) ;mkinode(entries0[str], cache_files[entries0[str]].meta, false, cache_files[entries0[str]].nlink, 0, cache_files[entries0[str]].size) ) = p_inode1 ∧ negdentry(str) = dent0 ∧ err = err0), entries0[str] = ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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