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Proof step 37 from proof inv-unlink (previous step)

# links(entries[str], dirs0) = m2, # links(m, dirs0) = dirs0[m].nlink, files[entries[str]] = mkfile(m0, md2, m2, content), dirs0[m] = mkdir(dirs0[m].size, md3, dirs0[m].nlink, dirs0[m].nsubdirs, entries), entries[str] = dirs0[m].entries[str], files[entries[str]] = mkfile(m1, md1, m2, content0), dirs = dirs0[m, (dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 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] ∈ files, str ∈ entries, m ∈ dirs0, str ∈ dirs0[m].entries, 1 ≤ dirs0[m].size, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, false, # links(entries[str], dirs0), 0, m3); 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(entries[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)))), dirs0[m].size = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# links(m, dirs0) = dirs0[m].nlink, entries[str] = dirs0[m].entries[str], dirs0[m] = mkdir(dirs0[m].size, md3, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries[str]] = mkfile(m1, md1, # links(entries[str], dirs0), content0), dirs = dirs0[m, (dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)], dirs0[m].size ≠ 0, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str ∈ dirs0[m].entries, m ∈ dirs0, str ∈ entries, entries[str] ∈ files, 1 ≤ dirs0[m].size, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, false, # links(entries[str], dirs0), 0, m3); 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(entries[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))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)