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Proof step 128 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), (m3 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), 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), dcache = dcache0 -- key, dcache0 = cache_dcache, err = ESUCCESS, key = dentrykey(p_ino, name), name = str, p_ino = m9, 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, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [dcache_set#(m3, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, dcache)] ( icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m3, mkientry(false, mkinode(m3, md5, true, m14, m15, m13))], 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 (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, m14, m15, m13))], 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, m14, m15, m13))], 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, m14, m15, m13) ;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, m14, m15, m13) ;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, m14, m15, m13) ;mkinode(m3, cache_files[m3].meta, false, cache_files[m3].nlink, 0, cache_files[m3].size) )) ] ∧ (afs_asynced ↔ asynced0))), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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