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Proof step 10 from proof inv-evict (previous step)

inode.nlink = 0, inode.nsubdirs = dirs[inode.ino].nsubdirs, inode.size = dirs[inode.ino].size, 0 = dirs[inode.ino].nlink, inode.directory, afs-cons(dirs, files), inode.ino ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE ⊦ inode.ino = ROOT_INO, (ino ≠ inode.ino ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- inode.ino) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ≠ inode.ino ∧ ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs -- inode.ino) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs -- inode.ino)) ∧ (ino ∈ files → (ino = inode.ino ∨ ¬ ino ∈ dirs) ∧ files[ino].nlink = # links(ino, dirs -- inode.ino)) ∧ ( ino ≠ inode.ino ∧ ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ≠ inode.ino ∧ dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
0 = dirs[m].nlink, boolvar, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = 0, m1 = dirs[m].nsubdirs, m2 = dirs[m].size, afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs -- m) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ≠ m ∧ ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs -- m) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs -- m)) ∧ (ino ∈ files → (ino = m ∨ ¬ ino ∈ dirs) ∧ files[ino].nlink = # links(ino, dirs -- m)) ∧ (ino ≠ m ∧ ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ≠ m ∧ dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files)

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] → [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: inode, m, md, boolvar, m0, m1, m2