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Proof step 507 from proof refine-rename-file-dentry (previous step)

(m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m3, m0) ;mkinode (m, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .size) ) = mkinode(m2, md5, boolvar, m4, m5, m6), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), cache_dirs[m] = mkdir(m0, md3, # links(m, cache_dirs), m3, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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), entries[str0] ∈ cache_files, str0 ∈ entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set#(mkinode(m, md0, true, # links(m, cache_dirs), m3, m0), false; err, cache_icache); icache_set# ((m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m3, m0) ;mkinode (m, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m ] .size) ), false ; err, cache_icache); str := str0; new_child_inode := (entries[str0] ∈ cache_dirs ⊃ mkinode (entries[str0], cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].meta, true, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].nlink, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].nsubdirs, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)][entries[str0]].size) ;mkinode (entries[str0], cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .size) ); entries0 := entries; if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete#(m2, mkdentry(str0, entries[str0]).name; err, cache_dcache); dcache_set# (m2, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ dcache-cons (cache_dcache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ pcache-cons (cache_pcache, cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ afs-cons (cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ synced(cache_dirs[m, mkdir(m0, md0, # links(m, cache_dirs), m3, entries)], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1], cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); old_parent_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m3, m0); 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_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m ∈ cache_dirs3 ⊃ mkinode(m, md0, true, # links(m, cache_dirs3), m3, m0) ;mkinode (m, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).meta, false, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).nlink, 0, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).size) ) = old_parent_inode0 ∧ (m ∈ cache_dirs3 ⊃ mkinode(m, md0, true, # links(m, cache_dirs3), m3, m0) ;mkinode (m, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).meta, false, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).nlink, 0, (m = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m]).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(str0, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3[m, mkdir(m0, md0, # links(m, cache_dirs3), m3, entries)] ∧ afs_files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0))), entries[str0] ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 508:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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), entries[str0] ∈ cache_files, str0 ∈ entries, m2 ∈ cache_dirs, ¬ entries[str0] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ [icache_set#(mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), false; err, cache_icache); icache_set# ((m2 ∈ cache_dirs ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6) ;mkinode (m2, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m2 ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m2 ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [m2 ] .size) ), false ; err, cache_icache); str := str0; new_child_inode := (entries[str0] ∈ cache_dirs ⊃ mkinode (entries[str0], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)][entries[str0]].meta, true, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)][entries[str0]].nlink, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)][entries[str0]].nsubdirs, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)][entries[str0]].size) ;mkinode (entries[str0], cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .meta, false, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .nlink, 0, cache_files [entries[str0], cache_files [entries[str0], cache_files[entries[str0]].size:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).size ] [entries[str0] ] .meta:= mkinode(entries[str0], md1, false, # links(entries[str0], cache_dirs), 0, m10).meta ] [entries[str0] ] .size) ); entries0 := entries; if mkdentry(str, entries0[str]).dentry? then icache_set#(new_child_inode, false; err, cache_icache); dcache_delete#(m2, mkdentry(str0, entries[str0]).name; err, cache_dcache); dcache_set# (m2, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ dcache-cons (cache_dcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ pcache-cons (cache_pcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ afs-cons (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1]) ∧ synced(cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1], cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries0[str]); old_dent0 := mkdentry(str0, entries[str0]); new_parent_inode0 := mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6); old_parent_inode0 := mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6); 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_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m2 ∈ cache_dirs3 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs3), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).size) ) = old_parent_inode0 ∧ (m2 ∈ cache_dirs3 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs3), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m10).meta:= md1;cache_files[m2]).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(str0, entries[str0]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs3[m2, mkdir(m6, md5, # links(m2, cache_dirs3), m5, entries)] ∧ afs_files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m10).meta:= md1] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)