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Proof step 41 from proof inv-rmdir (previous step)

dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs = dirs0[m, mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)], entries0[str] ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, 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, str ∈ entries0, m ∈ dirs0, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1); dirs, files); p_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) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, dent.name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 42:
dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs = dirs0[m, mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)], ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1); dirs, files); p_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) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, dent.name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_drop_nlink#(INO; DIRS, FILES) {if INO ∈ DIRS then DIRS[INO].nlink := DIRS[INO].nlink - 1; if INO ∈ FILES then FILES[INO].nlink := FILES[INO].nlink - 1 };