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Proof step 31 from proof crash-neutral-link (previous step)

# links(m, dirs) = dirs[m].nlink, entries0[str] = dirs[ino0].entries[str], dirs[ino1] = mkdir(m4, md3, # links(ino1, dirs), m6, entries0), dirs[m] = mkdir(dirs[m].size, md1, dirs[m].nlink, dirs[m].nsubdirs, entries), files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), dirs1 = dirs[m, (dirs[m].entries:= dirs[m].entries[str0, entries0[str]]).size:= (dirs[m].size + 1)], files0 = files, afs-cons(dirs, files), str ∈ entries0, str ∈ dirs[ino0].entries, ino0 ∈ dirs, entries0[str] ∈ files, m ∈ dirs, ino1 ∈ dirs, ¬ str0 ∈ dirs[m].entries, ¬ str0 ∈ entries, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs1, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size); dirs1, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3); 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 := getinode(mkdentry(str, entries0[str]).ino, dirs1, files); 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 32:
# links(m, dirs) = m2, files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), dirs[m] = mkdir(m1, md1, m2, m5, entries), dirs[ino1] = mkdir(m4, md3, # links(ino1, dirs), m6, entries0), entries0[str] = dirs[ino0].entries[str], dirs[m] = mkdir(m1, md2, m2, m5, entries1), dirs1 = dirs[m, (dirs[m].entries:= entries1[str0, entries0[str]]).size:= (m1 + 1)], files0 = files, afs-cons(dirs, files), ino1 ∈ dirs, m ∈ dirs, entries0[str] ∈ files, ino0 ∈ dirs, str ∈ dirs[ino0].entries, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟨afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs1, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, m2, m5, m1); dirs1, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3); 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 := getinode(mkdentry(str, entries0[str]).ino, dirs1, files); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, str0 ∈ entries1, str0 ∈ entries

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], m1, md2, m2, m5, entries1]

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], m1, md2, m2, m5, entries1