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Proof step 122 from proof refine-rename-dir-negdentry (previous step)

(m3 = m9 ⊃ mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str);mkdir(m6, md6, # links(m3, cache_dirs), m8, entries3)) = mkdir(m2, md2, m4, m5, entries), (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), asynced ↔ false, cache_dirs[entries0[str]] = mkdir(m7, md4, # links(entries0[str], cache_dirs), m10, entries1), cache_dirs[m3] = mkdir(m6, md6, # links(m3, cache_dirs), m8, entries3), cache_dirs[m9] = mkdir(m0 + 1, md3, # links(m9, cache_dirs), m1 + 1, entries0), err = ESUCCESS, icache = cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))], inode = ( m3 ∈ cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] ⊃ mkinode (m3, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, cache_dirs[m3, mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])] [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3 ] .meta:= md5 ] [m3 ] .meta, true, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, cache_dirs[m3, mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])] [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3 ] .meta:= md5 ] [m3 ] .nlink, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, cache_dirs[m3, mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])] [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3 ] .meta:= md5 ] [m3 ] .nsubdirs, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, cache_dirs[m3, mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])] [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3 ] .meta:= md5 ] [m3 ] .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].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), entries0[str] ∈ cache_dirs, m9 ∈ cache_dirs, str ∈ entries0, m3 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m3 = m9 → md5 = md0, (m9 = m3 ⊃ str ∈ entries0;true), ( m3 ∈ cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] ⊃ ((m9 = m3 ⊃ str ∈ entries0;true) ∧ str ∈ entries0 ∧ (m9 = m3 ⊃ str ∈ entries0;true)) ∧ ((m9 = m3 ⊃ str ∈ entries0;true) ∧ str ∈ entries0 ∧ (m9 = m3 ⊃ str ∈ entries0;true)) ∧ ((m9 = m3 ⊃ str ∈ entries0;true) ∧ str ∈ entries0 ∧ (m9 = m3 ⊃ str ∈ entries0;true)) ∧ (m9 = m3 ⊃ str ∈ entries0;true) ∧ str ∈ entries0 ∧ (m9 = m3 ⊃ str ∈ entries0;true) ;true ), links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [dcache_delete#(m9, mkdentry(str, entries0[str]).name; err, cache_dcache); dcache_set#(m3, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, cache_dcache)] ( icache-cons (icache[inode.ino, mkientry(asynced, inode)], cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ afs-cons (cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ synced (cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], icache[inode.ino, mkientry(asynced, inode)], cache_pcache) ∧ (cache_sync → synced(cache_files, icache[inode.ino, mkientry(asynced, inode)], cache_pcache)) → ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m3, md5, true, # links(m3, cache_dirs), m8, m6); old_parent_inode0 := mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1); old_child_inode0 := mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m10, m7); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; new_child_inode1 := new_child_inode0; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; cache_dirs5 := 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)⟩ ( (m9 ∈ cache_dirs5 ⊃ mkinode (m9, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .meta, true, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .nlink, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .nsubdirs, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs5 ⊃ mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode (entries0[str], md1, true, # links(entries0[str], cache_dirs0), cache_dirs1[entries0[str]].nsubdirs, cache_dirs2[entries0[str]].size) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, entries0[str]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs5 [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs5), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ∧ m9 ∈ cache_dirs5 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m3 ∈ cache_dirs5 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs5[m3]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ icache[inode.ino, mkientry(asynced, inode)] ∧ (afs_asynced ↔ asynced0))), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
(m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m3 = m9 ⊃ mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str);mkdir(m6, md6, # links(m3, cache_dirs), m8, entries3)) = mkdir(m2, md2, m4, m5, entries), cache_dirs[m9] = mkdir(m0 + 1, md3, # links(m9, cache_dirs), m1 + 1, entries0), cache_dirs[m3] = mkdir(m6, md6, # links(m3, cache_dirs), m8, entries3), cache_dirs[entries0[str]] = mkdir(m7, md4, # links(entries0[str], cache_dirs), m10, entries1), err = ESUCCESS, 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), m3 ∈ cache_dirs, str ∈ entries0, m9 ∈ cache_dirs, entries0[str] ∈ cache_dirs, ¬ str0 ∈ entries3, m3 = m9 → md5 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ [dcache_delete#(m9, str; err, cache_dcache); dcache_set#(m3, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, cache_dcache)] ( icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m3, mkientry (false, mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .size)) ], cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ afs-cons (cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_files) ∧ synced (cache_dirs [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .meta:= md5 ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m3, mkientry (false, mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .size)) ], cache_pcache) ∧ ( cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m3, mkientry (false, mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) .size)) ], cache_pcache)) → ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m3, md5, true, # links(m3, cache_dirs), m8, m6); old_parent_inode0 := mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1); old_child_inode0 := mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m10, m7); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; new_child_inode1 := new_child_inode0; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; cache_dirs5 := cache_dirs; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; 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)⟩ ( (m9 ∈ cache_dirs5 ⊃ mkinode (m9, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .meta, true, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .nlink, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .nsubdirs, (m9 = m3 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs5), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode0 ∧ (m3 ∈ cache_dirs5 ⊃ mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) = new_parent_inode0 ∧ mkinode (entries0[str], md1, true, # links(entries0[str], cache_dirs0), cache_dirs1[entries0[str]].nsubdirs, cache_dirs2[entries0[str]].size) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, entries0[str]) = new_dent0 ∧ err = err0 ∧ cache_dirs = cache_dirs5 [m9, (m9 = m3 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs5), m1, entries0 -- str) ) .meta:= md0 ] [m3, (m3 = m9 ∧ m9 ∈ cache_dirs5 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m3 ∈ cache_dirs5 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs5[m3]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [(m3 ∈ cache_dirs3 ⊃ mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) ) .ino, mkientry (false, (m3 ∈ cache_dirs3 ⊃ mkinode (m3, md5, true, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nlink, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .nsubdirs, (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ) .size) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) )) ] ∧ (afs_asynced ↔ asynced0)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ (ad.meta:= md).size = ad.size; (s)% ⊦ (ad.meta:= md).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.meta:= md).nlink = ad.nlink; (s)% ⊦ (ad.meta:= md).meta = md; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)