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Proof step 40 from proof afs-cons-rename-file-dentry (previous step)

# links(entries[str], dirs0) = files[entries[str]].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(m, dirs0) = dirs0[m].nlink, # links(entries0[str0], dirs0) = files[entries0[str0]].nlink, dirs0[m0].size = m3 + 1, dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries[str]] = mkfile(m1, md3, files[entries[str]].nlink, content), files[entries0[str0]] = mkfile(m4, md4, files[entries0[str0]].nlink, content0), dirs0[m0] = mkdir(m3 + 1, md6, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries0), entries[str] = dirs0[m].entries[str], entries0[str0] = dirs0[m0].entries[str0], dirs = dirs0[m0, (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3] [m, (m = m0 ⊃ (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3;dirs0[m]) .entries:= (m = m0 ⊃ (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3;dirs0[m]).entries[str, entries0[str0]] ], afs-cons(dirs0, files), str ∈ entries, str0 ∈ entries0, m ∈ dirs0, m0 ∈ dirs0, entries[str] ∈ files, entries0[str0] ∈ files, str ∈ dirs0[m].entries, str0 ∈ dirs0[m0].entries, ¬ entries0[str0] ∈ dirs0, ¬ entries[str] ∈ dirs0, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); old_dent := mkdentry(str0, entries0[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m0, md2, true, dirs0[m0].nlink, dirs0[m0].nsubdirs, m3 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); if asynced1 then {afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m2); dirs, files); new_child_inode := getinode(entries[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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), m0 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 41:
# links(entries0[str0], dirs0) = files[entries0[str0]].nlink, # links(m, dirs0) = dirs0[m].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(entries[str], dirs0) = m6, dirs0[m0].size = m3 + 1, entries0[str0] = dirs0[m0].entries[str0], entries[str] = dirs0[m].entries[str], dirs0[m0] = mkdir(m3 + 1, md6, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries0), files[entries0[str0]] = mkfile(m4, md4, files[entries0[str0]].nlink, content0), files[entries[str]] = mkfile(m1, md3, m6, content), dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries[str]] = mkfile(m5, md0, m6, content1), dirs = dirs0[m0, (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3] [m, (m = m0 ⊃ (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3;dirs0[m]) .entries:= (m = m0 ⊃ (dirs0[m0].entries:= (dirs0[m0].entries -- str0)).size:= m3;dirs0[m]).entries[str, entries0[str0]] ], afs-cons(dirs0, files), str0 ∈ dirs0[m0].entries, str ∈ dirs0[m].entries, entries0[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs0, m ∈ dirs0, str0 ∈ entries0, str ∈ entries, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); old_dent := mkdentry(str0, entries0[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m0, md2, true, dirs0[m0].nlink, dirs0[m0].nsubdirs, m3 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); if asynced1 then {afs_inode_sync#(mkinode(entries[str], md, false, # links(entries[str], dirs0), 0, m2); dirs, files); new_child_inode := getinode(entries[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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, entries[str] ∈ dirs0, m0 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0])

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[entries[str]], m5, md0, m6, 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[entries[str]], m5, md0, m6, content1