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Proof step 338 from proof afs-cons-rename-dir-dentry (previous step)

# links(m, dirs0) = dirs0[m].nlink, dirs0[entries1[str0]] = mkdir(m0, md0, # links(entries1[str0], dirs0), m2, ∅), dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[m] = mkdir(dirs0[m].size, md6, dirs0[m].nlink, dirs0[m].nsubdirs, entries1), entries[str0] = entries1[str0], entries1[str0] = dirs0[m].entries[str0], dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], entries1[str0] ≠ ROOT_INO, afs-cons(dirs0, files), str0 ∈ entries, str0 ∈ entries1, entries1[str0] ∈ dirs0, m ∈ dirs0, str0 ∈ dirs0[m].entries, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md2, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync# (mkinode(entries[str0], md, true, # links(entries[str0], dirs0), dirs0[entries[str0]].nsubdirs, dirs0[entries[str0]].size); dirs, files); new_child_inode := getinode(entries[str0], dirs, files); old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 339:
# links(m, dirs0) = m3, entries1[str0] = entries0[str0], entries[str0] = entries1[str0], dirs0[m] = mkdir(m1, md6, m3, m4, entries1), dirs0[m] = mkdir(m1, md4, m3, m4, entries), dirs0[entries1[str0]] = mkdir(m0, md0, # links(entries1[str0], dirs0), m2, ∅), dirs0[m] = mkdir(m1, md1, m3, m4, entries0), dirs = dirs0[m, dirs0[m].entries:= (entries0 -- str0).entries:= entries0], afs-cons(dirs0, files), str0 ∈ entries0, m ∈ dirs0, entries1[str0] ∈ dirs0, str0 ∈ entries1, str0 ∈ entries, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md2, true, m3, m4, m1); dirs, files); afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), m4, m1); dirs, files); afs_inode_sync# (mkinode(entries[str0], md, true, # links(entries[str0], dirs0), dirs0[entries[str0]].nsubdirs, dirs0[entries[str0]].size); dirs, files); new_child_inode := getinode(entries[str0], dirs, files); old_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), entries1[str0] = ROOT_INO

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] → [dirs0[m], m1, md1, m3, m4, 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: dirs0[m], m1, md1, m3, m4, entries0