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Proof step 21 from proof crash-neutral-unlink (previous step)

# links(m, dirs) = dirs[m].nlink, c_inode.ino = entries[str], c_inode.nlink = files[entries[str]].nlink, c_inode.nsubdirs = 0, entries[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md0, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs1 = dirs[m, (dirs[m].entries:= (dirs[m].entries -- str)).size:= (dirs[m].size - 1)], files0 = files, dirs[m].size ≠ 0, afs-cons(dirs, files), str ∈ entries, str ∈ dirs[m].entries, entries[str] ∈ files, m ∈ dirs, 1 ≤ dirs[m].size, ¬ c_inode.directory, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs1, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size); dirs1, files); afs_inode_sync#(c_inode; dirs1, files); p_inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs1 ⊃ mkinode(c_inode.ino, dirs1[c_inode.ino].meta, true, dirs1[c_inode.ino].nlink, dirs1[c_inode.ino].nsubdirs, dirs1[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# links(m, dirs) = m1, c_inode.ino = entries[str], c_inode.nlink = files[entries[str]].nlink, c_inode.nsubdirs = 0, dirs[m] = mkdir(m0, md0, m1, m2, entries), entries[str] = entries0[str], dirs[m] = mkdir(m0, md1, m1, m2, entries0), dirs1 = dirs[m, (dirs[m].entries:= (entries0 -- str)).size:= (m0 - 1)], files0 = files, afs-cons(dirs, files), m ∈ dirs, entries[str] ∈ files, str ∈ entries0, str ∈ entries, 1 ≤ m0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs1, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, m1, m2, m0); dirs1, files); afs_inode_sync#(c_inode; dirs1, files); p_inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs1 ⊃ mkinode(c_inode.ino, dirs1[c_inode.ino].meta, true, dirs1[c_inode.ino].nlink, dirs1[c_inode.ino].nsubdirs, dirs1[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, m0 = 0, c_inode.directory

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md, m1, m2, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md, m1, m2, entries0