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Proof step 65 from proof inv-rename-dir-negdentry (previous step)

# links(m, dirs0) = m4, # links(m0, dirs0) = dirs0[m0].nlink, # links(entries[str], dirs0) = dirs0[entries[str]].nlink, dirs0[entries[str]] = mkdir(dirs0[entries[str]].size, md5, dirs0[entries[str]].nlink, dirs0[entries[str]].nsubdirs, entries2), dirs0[m0] = mkdir(dirs0[m0].size, md4, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries1), dirs0[m] = mkdir(m1 + 1, md2, m4, m2 + 1, entries), entries[str] = entries0[str], dirs0[m] = mkdir(m3, md, m4, m5, entries0), dirs = dirs0[m, ((dirs0[m].entries:= (entries0 -- str)).size:= m1).nsubdirs:= m2] [m0, ( ( (m0 = m ⊃ ((dirs0[m].entries:= (entries0 -- str)).size:= m1).nsubdirs:= m2;dirs0[m0]) .entries:= (m0 = m ⊃ ((dirs0[m].entries:= (entries0 -- str)).size:= m1).nsubdirs:= m2;dirs0[m0]).entries[str0, entries[str]]) .size:= ((m0 = m ⊃ ((dirs0[m].entries:= (entries0 -- str)).size:= m1).nsubdirs:= m2;dirs0[m0]).size + 1)) .nsubdirs:= ((m0 = m ⊃ ((dirs0[m].entries:= (entries0 -- str)).size:= m1).nsubdirs:= m2;dirs0[m0]).nsubdirs + 1) ], m3 = m1 + 1, m5 = m2 + 1, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries[str] ∈ dirs0, m0 ∈ dirs0, m ∈ dirs0, str ∈ entries, str ∈ entries0, m0 = m → md1 = md0, asynced2 → synced(files, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, m4, m2 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), dirs0[m0].nsubdirs, dirs0[m0].size); dirs, files); skip; old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); skip; dcache_delete#(old_parent_inode.ino, mkdentry(str, entries[str]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(str0, mkdentry(str, entries[str]).ino).name, mkdentry(str0, mkdentry(str, entries[str]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), str0 ∈ dirs0[m0].entries, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
# links(entries0[str], dirs0) = dirs0[entries0[str]].nlink, # links(m0, dirs0) = dirs0[m0].nlink, dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries0), dirs0[m0] = mkdir(dirs0[m0].size, md4, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries1), dirs0[entries0[str]] = mkdir(dirs0[entries0[str]].size, md5, dirs0[entries0[str]].nlink, dirs0[entries0[str]].nsubdirs, entries2), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)] [m0, ( ( (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]) .entries:= (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]).entries[str0, entries0[str]]) .size:= ((m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]).size + 1)) .nsubdirs:= ((m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]).nsubdirs + 1) ], afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str ∈ entries0, m ∈ dirs0, m0 ∈ dirs0, entries0[str] ∈ dirs0, ¬ str0 ∈ entries1, ¬ str0 ∈ dirs0[m0].entries, asynced2 → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m2 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), dirs0[m0].nsubdirs, dirs0[m0].size); dirs, files); skip; old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); skip; dcache_delete#(old_parent_inode.ino, mkdentry(str, entries0[str]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nsubdirs:= m4 = mkdir(m, md, m0, m4, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base