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Proof step 14 from proof inv-mkdir (previous step)

dirs[m] = mkdir(m0, md2, # links(m, dirs), m2, entries0), dent = negdentry(str), p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, ¬ str ∈ entries0, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_mkdir#(md; p_inode, c_inode, dent, err, dirs, files; asynced0); 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, dent.name, 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)) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

Proof step 15:
afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files) ⊦ ⟪afs_mkdir#(md; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)
Proof step 16:
dirs[m] = mkdir(m0, md2, # links(m, dirs), m2, entries0), dent = negdentry(str), md1 = md, p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_mkdir#(md; p_inode, c_inode, 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, dent.name, 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)) ∧ afs-cons(dirs, files))), str ∈ entries0

Rule argument

spec: afs-asm name: inv-mkdir seq: afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files) ⊦ ⟪afs_mkdir# (md; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files) subst: [md, files, dirs, err, dent, c_inode, p_inode, asynced] → [md, files, dirs, err, dent, c_inode, p_inode, asynced0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ pre-mkdir(p_inode, dent, md, dirs, files) ↔ valid-negdentry(p_inode.ino, dent, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)