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Proof step 188 from proof refine-rename-file-dentry (previous step)

# 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), 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 = cache_icache[m15, mkientry(false, mkinode(m15, md, true, m16, m17, m))] [m3, mkientry (false, 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)) ], 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), str0 ∈ entries, str ∈ entries1, entries1[str] ∈ cache_files, m15 ∈ cache_dirs, entries[str0] ∈ cache_files, m3 ∈ cache_dirs, ¬ entries[str0] ∈ cache_dirs, ¬ entries1[str] ∈ cache_dirs, m3 = m15 → md10 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m15, cache_dirs) ≠ ∅ ∨ m15 = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [icache_set# (mkinode (entries1[str], 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 ] [entries1[str] ] .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 ] [entries1[str] ] .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 ] [entries1[str] ] .size), 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, entries1[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(entries1[str], md1, false, # links(entries1[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; cache_dirs1 := 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)⟩ ( (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 ∧ (entries1[str] ∈ cache_dirs1 ⊃ mkinode (entries1[str], (entries1[str] = m3 ⊃ (entries1[str] = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]) ;mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ) .meta:= md10 ;(entries1[str] = m15 ⊃ mkdir(m1, md0, # links(entries1[str], cache_dirs1), m6, entries -- str0);cache_dirs1[entries1[str]]) ) .meta, true, (entries1[str] = m3 ⊃ (entries1[str] = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]) ;mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ) .meta:= md10 ;(entries1[str] = m15 ⊃ mkdir(m1, md0, # links(entries1[str], cache_dirs1), m6, entries -- str0);cache_dirs1[entries1[str]]) ) .nlink, (entries1[str] = m3 ⊃ (entries1[str] = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]) ;mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ) .meta:= md10 ;(entries1[str] = m15 ⊃ mkdir(m1, md0, # links(entries1[str], cache_dirs1), m6, entries -- str0);cache_dirs1[entries1[str]]) ) .nsubdirs, (entries1[str] = m3 ⊃ (entries1[str] = m15 ⊃ mkdir(m5, md0, m9, m11, entries2[str, entries[str0]]) ;mkdir(m5, md8, m9, m11, entries2[str, entries[str0]]) ) .meta:= md10 ;(entries1[str] = m15 ⊃ mkdir(m1, md0, # links(entries1[str], cache_dirs1), m6, entries -- str0);cache_dirs1[entries1[str]]) ) .size) ;mkinode(entries1[str], md1, false, m14, 0, m10) ) = 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))), m15 = m3 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [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 ] [entries1[str] ], m18, md11, m19, content3]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: 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 ] [entries1[str] ], m18, md11, m19, content3