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Proof step 100 from proof crash-neutral-rmdir (previous step)

# links(m, dirs) = dirs[m].nlink, # links(entries[str], dirs) = c_inode.nlink, c_inode.ino = entries[str], dirs[m].size = 0, entries[str] = dirs[m].entries[str], dirs[m] = mkdir(0, md0, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[entries[str]] = mkdir(c_inode.size, md1, c_inode.nlink, c_inode.nsubdirs, ∅), entries[str] ≠ ROOT_INO, c_inode.directory, afs-cons(dirs, files), str ∈ dirs[m].entries, entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 101:
# links(entries[str], dirs) = m1, # links(m, dirs) = dirs[m].nlink, dirs[m].size = 0, dirs[entries[str]] = mkdir(m3, md1, m1, m2, ∅), dirs[m] = mkdir(0, md0, dirs[m].nlink, dirs[m].nsubdirs, entries), entries[str] = dirs[m].entries[str], boolvar, c_inode = mkinode(m0, md, boolvar, m1, m2, m3), m0 = entries[str], afs-cons(dirs, files), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, str ∈ dirs[m].entries, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, entries[str] = 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, md, 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, md, boolvar, m1, m2, m3