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

dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(m0, md4, # links(m, dirs), m7, entries2), files[entries1[str]] = mkfile(m1, md5, # links(entries1[str], dirs), content), entries0[str] = entries1[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries[str] = entries1[str], dirs[ino1] = mkdir(m5, md2, # links(ino1, dirs), m10, entries1), c_inode = mkinode(entries1[str], md0, false, # links(entries1[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, # links(m, dirs), m7, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries1[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ino0 ∈ dirs, str ∈ entries, ino1 ∈ dirs, str ∈ entries1, ¬ str0 ∈ entries2, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced0)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 38:
dirs[ino1] = mkdir(m5, md2, # links(ino1, dirs), m10, entries1), entries[str] = entries1[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries0[str] = entries1[str], files[entries1[str]] = mkfile(m1, md5, # links(entries1[str], dirs), content), dirs[m] = mkdir(m0, md4, # links(m, dirs), m7, entries2), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), c_inode = mkinode(entries1[str], md0, false, # links(entries1[str], dirs), 0, m3), new_dent = negdentry(str0), old_dent = mkdentry(str, entries0[str]), p_inode = mkinode(m, md, true, # links(m, dirs), m7, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries1, ino1 ∈ dirs, str ∈ entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries1[str] ∈ files, asynced1 → synced(files, icache, pcache), links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [if pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries[new_dent.name] := old_dent.ino; dirs[p_ino].size := dirs[p_ino].size + 1; let ino = old_dent.ino in afs_inc_nlink#(ino; dirs, files); new_dent := mkdentry(new_dent.name, old_dent.ino); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(old_dent.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; 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)))), str0 ∈ entries2

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_link# (OLD_DENT; P_INODE, C_INODE, NEW_DENT, ERR, DIRS, FILES; ASYNCED) {if pre-link(P_INODE, C_INODE, OLD_DENT, NEW_DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries[NEW_DENT.name] := OLD_DENT.ino; DIRS[P_INO].size := DIRS[P_INO].size + 1; let INO = OLD_DENT.ino in afs_inc_nlink#(INO; DIRS, FILES); NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); afs_inode_sync#(P_INODE; DIRS, FILES); afs_inode_sync#(C_INODE; DIRS, FILES); P_INODE := getinode(P_INODE.ino, DIRS, FILES); C_INODE := getinode(OLD_DENT.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };