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Proof step 11 from proof crash-neutral-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 ⊦ inode.ino = ROOT_INO, dirs \ orphans(dirs, files) = (dirs -- inode.ino) \ orphans(dirs -- inode.ino, files) ∧ files \ orphans(dirs, files) = files \ orphans(dirs -- inode.ino, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
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), m ∈ dirs ⊦ m = ROOT_INO, dirs \ orphans(dirs, files) = (dirs -- m) \ orphans(dirs -- m, files) ∧ files \ orphans(dirs, files) = files \ orphans(dirs -- m, 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