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Proof step 7 from proof inv-link (previous step)

c_inode.ino = dirs[ino].entries[str], c_inode.nlink = files[c_inode.ino].nlink, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, new_dent = negdentry(str0), p_inode.directory, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), c_inode.ino ∈ files, p_inode.ino ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, ¬ c_inode.directory, ¬ str0 ∈ dirs[p_inode.ino].entries, asynced → synced(files, icache, pcache), links(c_inode.ino, dirs) ≠ ∅ ∨ c_inode.ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
c_inode.ino = dirs[ino].entries[str], c_inode.nlink = files[c_inode.ino].nlink, c_inode.nsubdirs = 0, boolvar, m0 = dirs[m].nlink, m1 = dirs[m].nsubdirs, m2 = dirs[m].size, new_dent = negdentry(str0), p_inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, c_inode.ino ∈ files, asynced → synced(files, icache, pcache), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(c_inode.ino, dirs) ≠ ∅ ∨ c_inode.ino = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( 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)), c_inode.directory, str0 ∈ dirs[m].entries

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m, md, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m, md, boolvar, m0, m1, m2