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Proof step 96 from proof refine-unlink (previous step)

# links(entries[str], cache_dirs) = m0 + 1, cache_dirs[m] = mkdir(m1 + 1, md4, # links(m, cache_dirs), m4, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, m0 + 1, content0), cache_files[entries[str]] = mkfile(m2, md3, m0 + 1, content), 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set# (getinode (entries[str], cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_files [entries[str], cache_files[entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]].size:= m6][entries[str]].meta:= md0 ]), false ; err, cache_icache); icache_set# ((m ∈ cache_dirs ⊃ mkinode(m, md, true, # links(m, cache_dirs), m4, m1) ;mkinode (m, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .meta, false, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .nlink, 0, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .size) ), false ; err, cache_icache); dcache_delete# ((m ∈ cache_dirs ⊃ mkinode(m, md, true, # links(m, cache_dirs), m4, m1) ;mkinode (m, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .meta, false, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .nlink, 0, cache_files [entries[str], cache_files [entries[str], cache_files[entries[str], mkfile(m2, md3, m0, content)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .size) ) .ino, mkdentry(str, entries[str]).name ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]) ∧ dcache-cons (cache_dcache, cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]) ∧ pcache-cons (cache_pcache, cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]) ∧ synced(cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files[entries[str], mkfile(m6, md0, m0, content)], cache_icache, cache_pcache)) ∧ afs-cons (cache_dirs[m, mkdir(m1, md, # links(m, cache_dirs), m4, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]) → ⟨dent0 := mkdentry(str, entries[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m4, m1 + 1); p_inode1 := mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_unlink#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2[m, mkdir(m1, md, # links(m, cache_dirs2), m4, entries -- str)] ∧ afs_files = (cache_files[entries[str], mkfile(m6, md0, m0, content)] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2 ⊃ mkinode(m, md, true, # links(m, cache_dirs2), m4, m1) ;mkinode (m, (m = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m]).meta, false, (m = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m]).nlink, 0, (m = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m]).size) ) = p_inode0 ∧ (entries[str] ∈ cache_dirs3 ⊃ mkinode (entries[str], (entries[str] = m ⊃ mkdir(m1, md, # links(entries[str], cache_dirs3), m4, entries -- str);cache_dirs3[entries[str]]).meta, true, (entries[str] = m ⊃ mkdir(m1, md, # links(entries[str], cache_dirs3), m4, entries -- str);cache_dirs3[entries[str]]).nlink, (entries[str] = m ⊃ mkdir(m1, md, # links(entries[str], cache_dirs3), m4, entries -- str);cache_dirs3[entries[str]]).nsubdirs, (entries[str] = m ⊃ mkdir(m1, md, # links(entries[str], cache_dirs3), m4, entries -- str);cache_dirs3[entries[str]]).size) ;mkinode(entries[str], md0, false, m0, 0, m6) ) = p_inode1 ∧ negdentry(str) = dent0 ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(m ∈ cache_dirs ⊃ mkinode(m, md, true, # links(m, cache_dirs), m4, m1) ;mkinode (m, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .meta, false, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .nlink, 0, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .size) ), m3, md1, boolvar, m5, m8, m9]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (m ∈ cache_dirs ⊃ mkinode(m, md, true, # links(m, cache_dirs), m4, m1) ;mkinode (m, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .meta, false, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .nlink, 0, cache_files [entries[str], cache_files [entries[str], cache_files [entries[str], mkfile(m2, md3, m0, content) ] [entries[str] ] .size:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .size ] [entries[str] ] .meta:= mkinode (entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) .meta ] [m ] .size) ), m3, md1, boolvar, m5, m8, m9