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Proof step 232 from proof afs-cons-rename-file-dentry (previous step)

# links(entries0[str0], dirs0) = files[entries0[str0]].nlink, # links(m, dirs0) = dirs0[m].nlink, dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries0[str0]] = mkfile(m1, md3, files[entries0[str0]].nlink, content), files[entries0[str0]] = mkfile(m4, md4, files[entries0[str0]].nlink, content0), 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 233:
# links(m, dirs0) = dirs0[m].nlink, # links(entries0[str0], dirs0) = m3, entries0[str0] = dirs0[m].entries[str0], entries[str0] = entries0[str0], dirs0[m] = mkdir(dirs0[m].size, md6, dirs0[m].nlink, dirs0[m].nsubdirs, entries0), files[entries0[str0]] = mkfile(m4, md4, m3, content0), files[entries0[str0]] = mkfile(m1, md3, m3, content), dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries0[str0]] = mkfile(m0, md0, m3, content1), dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], afs-cons(dirs0, files), str0 ∈ dirs0[m].entries, entries0[str0] ∈ files, m ∈ dirs0, str0 ∈ entries0, str0 ∈ 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, 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-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries0[str0]], m0, md0, m3, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries0[str0]], m0, md0, m3, content1