[Imprint][Data Privacy Statement][E-Mail]

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Proof step 186 from proof refine-rename-file-dentry (previous step)

# links(entries1[str], cache_dirs) = m14 + 1, (m3 = m15 ⊃ mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0);mkdir(m0, md9, # links(m3, cache_dirs), m7, entries1)) = mkdir(m5, md8, m9, m11, entries2), (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md0, # links(m15, cache_dirs), m6, entries -- str0)) = mkdir(m, md, m16, m17, entries3), asynced ↔ false, cache_files[entries[str0]] = mkfile(m4, md5, # links(entries[str0], cache_dirs), content2), cache_dirs[m3] = mkdir(m0, md9, # links(m3, cache_dirs), m7, entries1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m12, md3, m14 + 1, content), cache_dirs[m15] = mkdir(m1 + 1, md6, # links(m15, cache_dirs), m6, entries), cache_files[entries1[str]] = mkfile(m2, md7, m14 + 1, content1), cache_icache0 = icache[inode.ino, mkientry(asynced, inode)], entries0 = entries1, err = ESUCCESS, icache = cache_icache[m15, mkientry(false, mkinode(m15, md, true, m16, m17, m))], inode = ( m3 ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] ⊃ mkinode (m3, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .meta, true, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .nlink, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .nsubdirs, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .size) ;mkinode (m3, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .meta, false, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .nlink, 0, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .size) ), new_child_inode = ( entries1[str] ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ⊃ mkinode (entries1[str], cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .meta, true, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .nlink, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .nsubdirs, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .size) ;mkinode (entries1[str], cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .meta, false, cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .nlink, 0, cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .size) ), 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), m3 ∈ cache_dirs, entries[str0] ∈ cache_files, m15 ∈ cache_dirs, entries1[str] ∈ cache_files, str ∈ entries1, str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m15 → md10 = md0, ( m3 ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] ⊃ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ (m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries ; (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ), (m15 = m3 ⊃ str0 ∈ entries;true), ( entries1[str] ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ⊃ str ∈ entries1 ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1 ; str ∈ entries1 ∧ ( ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ ( ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m15, cache_dirs) ≠ ∅ ∨ m15 = ROOT_INO ⊦ [if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache0); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, cache_dcache); dcache_set# (m3, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache0, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ dcache-cons (cache_dcache, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ pcache-cons (cache_pcache, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ afs-cons (cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ synced (cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_icache0, cache_pcache) ∧ (cache_sync → synced(cache_files[entries1[str], mkfile(m10, md1, m14, content1)], cache_icache0, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m3, md10, true, # links(m3, cache_dirs), m7, m0); old_parent_inode0 := mkinode(m15, md0, true, # links(m15, cache_dirs), m6, m1 + 1); new_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m15 ∈ cache_dirs3 ⊃ mkinode (m15, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .meta, true, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .nlink, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .nsubdirs, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .size) ;mkinode (m15, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).meta, false, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).nlink, 0, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs3 ⊃ mkinode (m3, md10, true, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).nlink, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).nsubdirs, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).size) ;mkinode (m3, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).meta, false, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).nlink, 0, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).size) ) = new_parent_inode0 ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3 [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs3), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ∧ afs_files = (cache_files[entries1[str], mkfile(m10, md1, m14, content1)] ⊕ cache_pcache) ⊕ cache_icache0 ∧ (afs_asynced ↔ asynced0))), entries1[str] ∈ cache_dirs, entries[str0] ∈ cache_dirs, m15 = m3 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 187:
# links(entries1[str], cache_dirs) = m14 + 1, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md0, # links(m15, cache_dirs), m6, entries -- str0)) = mkdir(m, md, m16, m17, entries3), (m3 = m15 ⊃ mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0);mkdir(m0, md9, # links(m3, cache_dirs), m7, entries1)) = mkdir(m5, md8, m9, m11, entries2), asynced ↔ false, cache_files[entries1[str]] = mkfile(m2, md7, m14 + 1, content1), cache_dirs[m15] = mkdir(m1 + 1, md6, # links(m15, cache_dirs), m6, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m12, md3, m14 + 1, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), cache_dirs[m3] = mkdir(m0, md9, # links(m3, cache_dirs), m7, entries1), cache_files[entries[str0]] = mkfile(m4, md5, # links(entries[str0], cache_dirs), content2), cache_icache0 = icache[inode.ino, mkientry(asynced, inode)], entries0 = entries1, err = ESUCCESS, icache = cache_icache[m15, mkientry(false, mkinode(m15, md, true, m16, m17, m))], inode = ( m3 ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] ⊃ mkinode (m3, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .meta, true, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .nlink, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .nsubdirs, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [m3 ] .size) ;mkinode (m3, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .meta, false, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .nlink, 0, cache_files [entries1[str], cache_files[entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]].size:= m10][entries1[str]].meta:= md1 ] [m3 ] .size) ), new_child_inode = ( entries1[str] ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ⊃ mkinode (entries1[str], cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .meta, true, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .nlink, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .nsubdirs, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] [entries1[str] ] .size) ;mkinode (entries1[str], cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .meta, false, cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .nlink, 0, cache_files [entries1[str], cache_files [entries1[str], cache_files[entries1[str], mkfile(m2, md7, m14, content1)][entries1[str]] .size:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md1, false, # links(entries1[str], cache_dirs), 0, m10).meta ] [entries1[str] ] .size) ), 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), str0 ∈ entries, str ∈ entries1, entries1[str] ∈ cache_files, m15 ∈ cache_dirs, entries[str0] ∈ cache_files, m3 ∈ cache_dirs, m3 = m15 → md10 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), ( entries1[str] ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ⊃ str ∈ entries1 ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ (((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ str ∈ entries1 ; str ∈ entries1 ∧ ( ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ ( ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ ( str ∈ entries1 ∧ ((str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ), (m15 = m3 ⊃ str0 ∈ entries;true), ( m3 ∈ cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]);mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0)).meta:= md0 ] ⊃ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ ((m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries) ∧ (m15 = m3 ⊃ str0 ∈ entries;true) ∧ str0 ∈ entries ; (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ (str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1) ∧ str ∈ entries1 ∧ (str ∈ entries1 ∧ str ∈ entries1 ∧ str ∈ entries1) ∧ str ∈ entries1 ), links(m15, cache_dirs) ≠ ∅ ∨ m15 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [icache_set#(new_child_inode, false; err, cache_icache0); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, cache_dcache); dcache_set# (m3, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache0, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ dcache-cons (cache_dcache, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ pcache-cons (cache_pcache, cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ afs-cons (cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_files[entries1[str], mkfile(m10, md1, m14, content1)]) ∧ synced (cache_dirs [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ], cache_icache0, cache_pcache) ∧ (cache_sync → synced(cache_files[entries1[str], mkfile(m10, md1, m14, content1)], cache_icache0, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m3, md10, true, # links(m3, cache_dirs), m7, m0); old_parent_inode0 := mkinode(m15, md0, true, # links(m15, cache_dirs), m6, m1 + 1); new_child_inode0 := mkinode(entries0[str], md1, false, # links(entries0[str], cache_dirs), 0, m10); old_child_inode0 := mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m15 ∈ cache_dirs3 ⊃ mkinode (m15, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .meta, true, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .nlink, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .nsubdirs, (m15 = m3 ⊃ mkdir(m5, md10, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md0, # links(m15, cache_dirs3), m6, entries -- str0) ) .size) ;mkinode (m15, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).meta, false, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).nlink, 0, (m15 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m15]).size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs3 ⊃ mkinode (m3, md10, true, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).nlink, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).nsubdirs, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).size) ;mkinode (m3, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).meta, false, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).nlink, 0, (m3 = entries1[str] ⊃ mkfile(m10, md1, m14, content1);cache_files[m3]).size) ) = new_parent_inode0 ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3 [m15, (m15 = m3 ⊃ mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ;mkdir(m1, md6, # links(m15, cache_dirs3), m6, entries -- str0) ) .meta:= md0 ] [m3, (m3 = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]);mkdir(m5, md8, m9, m11, entries2[str, entries[str0]])).meta:= md10 ] ∧ afs_files = (cache_files[entries1[str], mkfile(m10, md1, m14, content1)] ⊕ cache_pcache) ⊕ cache_icache0 ∧ (afs_asynced ↔ asynced0))), entries[str0] ∈ cache_dirs, entries1[str] ∈ cache_dirs, m15 = m3 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)