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

dirs[c_inode.ino].entries = ∅, c_inode.ino = dirs[m].entries[str], c_inode.nlink = dirs[c_inode.ino].nlink, c_inode.nsubdirs = dirs[c_inode.ino].nsubdirs, c_inode.size = dirs[c_inode.ino].size, dent = mkdentry(str, c_inode.ino), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), c_inode.ino ≠ ROOT_INO, c_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 ∈ dirs, str ∈ dirs[m].entries, m ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rmdir#(; p_inode, c_inode, 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:
dirs[m0].entries = ∅, boolvar, c_inode = mkinode(m0, md0, boolvar, m1, m2, m3), dent = mkdentry(str, m0), m0 = dirs[m].entries[str], m1 = dirs[m0].nlink, m2 = dirs[m0].nsubdirs, m3 = dirs[m0].size, p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), 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 ∈ dirs[m].entries, m0 ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_rmdir#(; p_inode, c_inode, 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)), m0 = ROOT_INO

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] → [c_inode, m0, md0, boolvar, m1, m2, m3]

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: c_inode, m0, md0, boolvar, m1, m2, m3