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Proof step 132 from proof refine-rmdir (previous step)

(entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), (entries3[str] = m6 ⊃ mkdir(m0, md6, # links(entries3[str], cache_dirs), m1, entries3 -- str) ;mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (m6 = entries3[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs), m1, entries3 -- str)) = mkdir(m4, md3, m14, m15, entries0), cache_dirs[entries3[str]] = mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅), cache_dirs[m6] = mkdir(m0 + 1, md6, # links(m6, cache_dirs), m1 + 1, entries3), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m6, mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)], files = afs_files, ino = mkdentry(str, entries3[str]).ino, mkdentry(str, entries3[str]).dentry?, afs-cons (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons (cache_dcache -- dentrykey(m6, str), cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_pcache), m6 ∈ cache_dirs, entries3[str] ∈ cache_dirs, str ∈ entries3, cache_sync → synced (cache_files, cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ ⟨dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries3[str]).name); afs_inode_sync#(mkinode(m6, md, true, # links(m6, cache_dirs), m1 + 1, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries3[str], md0, true, # links(entries3[str], cache_dirs), m13, m2); dirs, files); p_inode := (m6 ∈ dirs ⊃ mkinode(m6, dirs[m6].meta, true, dirs[m6].nlink, dirs[m6].nsubdirs, dirs[m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ); c_inode := getinode(entries3[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs [m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md ] [entries3[str], (entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ] ∧ (asynced ↔ asynced0) ∧ mkinode(m6, md3, true, m14, m15, m4) = p_inode ∧ mkinode(entries3[str], md0, true, m8, m9, m) = c_inode ∧ negdentry(str) = dent ∧ ESUCCESS = err), entries3[str] = ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic