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Proof step 234 from proof afs-cons-rename-file-dentry (previous step)

# links(m, dirs0) = dirs0[m].nlink, dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries0[str0]] = mkfile(m0, md0, # links(entries0[str0], dirs0), content1), dirs0[m] = mkdir(dirs0[m].size, md6, dirs0[m].nlink, dirs0[m].nsubdirs, entries0), entries[str0] = entries0[str0], entries0[str0] = dirs0[m].entries[str0], dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], afs-cons(dirs0, files), str0 ∈ entries, str0 ∈ entries0, m ∈ dirs0, entries0[str0] ∈ files, str0 ∈ dirs0[m].entries, ¬ entries0[str0] ∈ dirs0, 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, false, # links(entries[str0], dirs0), 0, m2); 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 235:
# links(m, dirs0) = m3, entries0[str0] = entries1[str0], entries[str0] = entries0[str0], dirs0[m] = mkdir(m1, md6, m3, m4, entries0), files[entries0[str0]] = mkfile(m0, md0, # links(entries0[str0], dirs0), content1), dirs0[m] = mkdir(m1, md5, m3, m4, entries), dirs0[m] = mkdir(m1, md1, m3, m4, entries1), dirs = dirs0[m, dirs0[m].entries:= (entries1 -- str0).entries:= entries1], afs-cons(dirs0, files), str0 ∈ entries1, entries0[str0] ∈ files, m ∈ dirs0, str0 ∈ entries0, 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, false, # links(entries[str0], dirs0), 0, m2); 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), entries0[str0] ∈ dirs0

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, 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: dirs0[m], m1, md1, m3, m4, entries1