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Proof step 88 from proof refine-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m0, md1, # links(entries0[str], cache_dirs), m1, entries0 -- str) ;mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), cache_dirs[entries0[str]] = mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0 + 1, md1, # links(m, cache_dirs), m1 + 1, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, entries0[str] ≠ ROOT_INO, 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 ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set# (getinode (entries0[str], cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ], cache_files), false ; err, cache_icache); icache_set# (( m ∈ cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] ⊃ mkinode (m, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .meta, true, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nlink, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nsubdirs, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), false ; err, cache_icache); dcache_delete# (( m ∈ cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] ⊃ mkinode (m, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .meta, true, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nlink, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nsubdirs, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ synced (cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons (cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) → ⟨dent0 := mkdentry(str, entries0[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); p_inode1 := mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_rmdir#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2 [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs2), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ∧ entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md, m3, m7, entries) ;(entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md2, m3, m7, entries);cache_dirs2[entries0[str]]) ) .meta:= md0 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2 ⊃ mkinode (m, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).meta, true, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).nlink, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).nsubdirs, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs3 ⊃ mkinode (entries0[str], md0, true, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).nlink, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).nsubdirs, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).size) ;mkinode(entries0[str], cache_files[entries0[str]].meta, false, cache_files[entries0[str]].nlink, 0, cache_files[entries0[str]].size) ) = p_inode1 ∧ negdentry(str) = dent0 ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 89:
(entries0[str] = m ⊃ mkdir(m0, md1, # links(entries0[str], cache_dirs), m1, entries0 -- str) ;mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (m ∈ cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] ⊃ mkinode (m, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .meta, true, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nlink, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nsubdirs, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = mkinode(m6, md4, boolvar, m8, m9, m10), cache_dirs[m] = mkdir(m0 + 1, md1, # links(m, cache_dirs), m1 + 1, entries0), cache_dirs[entries0[str]] = mkdir(m2, md3, # links(entries0[str], cache_dirs), m4, ∅), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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), entries0[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [icache_set# (getinode (entries0[str], cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ], cache_files), false ; err, cache_icache); icache_set# (( m ∈ cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] ⊃ mkinode (m, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .meta, true, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nlink, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .nsubdirs, cache_dirs[m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2).meta ] [m ] .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), false ; err, cache_icache); dcache_delete#(m6, mkdentry(str, entries0[str]).name; err, cache_dcache)] ( icache-cons (cache_icache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ dcache-cons (cache_dcache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ pcache-cons (cache_pcache, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) ∧ synced (cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons (cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ], cache_files) → ⟨dent0 := mkdentry(str, entries0[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); p_inode1 := mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_rmdir#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2 [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, # links(m, cache_dirs2), m1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m ∧ entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md, m3, m7, entries) ;(entries0[str] ∈ cache_dirs2 ⊃ mkdir(m5, md2, m3, m7, entries);cache_dirs2[entries0[str]]) ) .meta:= md0 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2 ⊃ mkinode (m, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).meta, true, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).nlink, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).nsubdirs, (m = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m, cache_dirs2), m1, entries0 -- str)).size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs3 ⊃ mkinode (entries0[str], md0, true, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).nlink, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).nsubdirs, (entries0[str] = m ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).size) ;mkinode(entries0[str], cache_files[entries0[str]].meta, false, cache_files[entries0[str]].nlink, 0, cache_files[entries0[str]].size) ) = p_inode1 ∧ negdentry(str) = dent0 ∧ err = err0)), entries0[str] = ROOT_INO

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 [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] ⊃ mkinode (m, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs [entries0[str], mkdir(m5, md2, m3, m7, entries) ] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .meta, true, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs [entries0[str], mkdir(m5, md2, m3, m7, entries) ] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .nlink, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs [entries0[str], mkdir(m5, md2, m3, m7, entries) ] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .nsubdirs, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs [entries0[str], mkdir(m5, md2, m3, m7, entries) ] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .size) ;mkinode (m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), m6, md4, boolvar, m8, m9, m10]

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 [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] ⊃ mkinode (m, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .meta, true, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .nlink, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .nsubdirs, cache_dirs [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str], cache_dirs[entries0[str], mkdir(m5, md2, m3, m7, entries)] [m, (m = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries) ;mkdir (m0, md1, # links(m, cache_dirs), m1, entries0 -- str) ) .meta:= md ] [entries0[str] ] .meta:= mkinode (entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m2) .meta ] [m ] .size) ;mkinode (m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), m6, md4, boolvar, m8, m9, m10