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Proof step 28 from proof inv-create (previous step)

# links(m, dirs0) = dirs0[m].nlink, dirs0[m] = mkdir(dirs0[m].size, md1, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino] = mkdir(m0, md2, m1, m2, entries0), dent = negdentry(str), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino].size:= (m0 + 1) ], files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], p_ino = m, p_inode = mkinode(m, md0, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(p_inode; dirs, files); p_inode := (p_inode.ino ∈ dirs ⊃ mkinode(p_inode.ino, dirs[p_inode.ino].meta, true, dirs[p_inode.ino].nlink, dirs[p_inode.ino].nsubdirs, dirs[p_inode.ino].size) ;mkinode(p_inode.ino, files[p_inode.ino].meta, false, files[p_inode.ino].nlink, 0, files[p_inode.ino].size) ); c_inode := getinode(mkdentry(dent.name, ino).ino, dirs, files); asynced := ?] ( afs-cons(dirs, files) → ⟪if ESUCCESS = ESUCCESS then let asynced = false in {err := ESUCCESS; icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, mkdentry(dent.name, ino).name, mkdentry(dent.name, ino); 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)))), ino = 0, str ∈ dirs0[m].entries, str ∈ entries, ino ∈ files0, ino ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# links(m, dirs0) = dirs0[m].nlink, dirs0[m].entries:= dirs0[m].entries[str, ino] = mkdir(m0, md2, m1, m2, entries0), dirs0[m] = mkdir(dirs0[m].size, md1, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs = dirs0[m, mkdir(m0 + 1, md2, m1, m2, entries0)], files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], ino ≠ 0, afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ str ∈ dirs0[m].entries, ¬ str ∈ entries, ¬ ino ∈ files0, ¬ ino ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); 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(mkdentry(str, ino).ino, dirs, files); asynced := ?] ( afs-cons(dirs, files) → ⟪let asynced = false in {err := ESUCCESS; icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, str, mkdentry(str, ino); 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: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%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% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ negdentry(str).name = str; (s)