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Proof step 69 from proof inv-rename-dir-negdentry (previous step)

# links(m0, dirs0) = dirs0[m0].nlink, (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]) = mkdir(m4, md3, m6, m7, entries2), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m0] = mkdir(dirs0[m0].size, md4, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries1), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries0), 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:= entries2[str0, entries0[str]]) .size:= (m4 + 1)) .nsubdirs:= (m7 + 1) ], afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str] ∈ dirs0, m0 ∈ dirs0, m ∈ dirs0, 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, # 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)))), str0 ∈ dirs0[m0].entries, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
# links(m0, dirs0) = dirs0[m0].nlink, (m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str);dirs0[m0]) = mkdir(m4, md3, m6, m7, entries2), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m0] = mkdir(dirs0[m0].size, md4, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries1), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries0), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)][m0, mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])], afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str] ∈ dirs0, m0 ∈ dirs0, m ∈ dirs0, str ∈ entries0, ¬ str0 ∈ dirs0[m0].entries, ¬ str0 ∈ entries1, 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, # 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)