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Proof step 33 from proof inv-evict (previous step)

inode.nlink = 0, inode.nsubdirs = 0, 0 = files[inode.ino].nlink, files[ino] = mkfile(m, md, m0, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, inode.ino ∈ files, 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 ∧ m0 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files ⊦ inode.ino = ROOT_INO, inode.directory, inode.ino ∈ dirs, (ino ≠ inode.ino ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ≠ inode.ino ∧ dirs[ino].entries[name] ∈ files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
0 = files[m1].nlink, files[ino] = mkfile(m, md, m0, content), ¬ boolvar, inode = mkinode(m1, md0, boolvar, m2, m3, m4), m2 = 0, m3 = 0, afs-cons(dirs, files), m1 ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # 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 = ∅ ⊦ m1 = ROOT_INO, m1 ∈ dirs, (ino ≠ m1 ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ≠ m1 ∧ 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, m1, md0, boolvar, m2, m3, m4]

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, m1, md0, boolvar, m2, m3, m4