[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 22 from proof inv-rename-dentry (previous step)

entries[str] ∈ files ↔ entries0[str0] ∈ files, dirs[m0] = mkdir(m12, md6, # links(m0, dirs), m15, entries0), files[entries0[str0]] = mkfile(m9, md4, m10, content0), files[entries[str]] = mkfile(m1, md3, m8, content), dirs[m] = mkdir(m11, md5, # links(m, dirs), m13, entries), dirs[entries[str]] = mkdir(m14, md7, m16, m17, entries1), new_child_inode = mkinode(entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m13, m11), old_child_inode = mkinode(entries0[str0], md2, boolvar0, m5, m6, m7), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m15, m12), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ dirs, m ∈ dirs, str0 ∈ entries0, str ∈ entries, asynced → synced(files, icache, pcache), m = m0 → md = md0, entries[str] ∈ dirs → entries[str] ≠ ROOT_INO ∧ entries1 = ∅, entries0[str0] ∈ dirs ∧ m5 = dirs[entries0[str0]].nlink ∧ m7 = dirs[entries0[str0]].size ∧ m6 = dirs[entries0[str0]].nsubdirs ∧ boolvar0 ∨ entries0[str0] ∈ files ∧ m5 = m10 ∧ m6 = 0 ∧ ¬ boolvar0, entries[str] ∈ dirs ∧ m2 = m16 ∧ m4 = m14 ∧ m3 = m17 ∧ boolvar ∨ entries0[str0] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, entries0[str0] ∈ dirs ∨ entries0[str0] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries[str] ∈ dirs ∨ entries0[str0] ∈ files ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
entries[str] ∈ files ↔ entries0[str0] ∈ files, dirs[entries[str]] = mkdir(m14, md7, m16, m17, entries1), dirs[m] = mkdir(m11, md5, # links(m, dirs), m13, entries), files[entries[str]] = mkfile(m1, md3, m8, content), files[entries0[str0]] = mkfile(m9, md4, m10, content0), dirs[m0] = mkdir(m12, md6, # links(m0, dirs), m15, entries0), dirs[entries0[str0]] = mkdir(m18, md8, m19, m20, entries2), new_child_inode = mkinode(entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m13, m11), old_child_inode = mkinode(entries0[str0], md2, boolvar0, m5, m6, m7), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md0, true, # links(m0, dirs), m15, m12), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ dirs → entries[str] ≠ ROOT_INO ∧ entries1 = ∅, m = m0 → md = md0, asynced → synced(files, icache, pcache), entries[str] ∈ dirs ∨ entries0[str0] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, entries0[str0] ∈ dirs ∨ entries0[str0] ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, entries[str] ∈ dirs ∧ m2 = m16 ∧ m4 = m14 ∧ m3 = m17 ∧ boolvar ∨ entries0[str0] ∈ files ∧ m2 = m8 ∧ m3 = 0 ∧ ¬ boolvar, entries0[str0] ∈ dirs ∧ m5 = m19 ∧ m7 = m18 ∧ m6 = m20 ∧ boolvar0 ∨ entries0[str0] ∈ files ∧ m5 = m10 ∧ m6 = 0 ∧ ¬ boolvar0 ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

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[entries0[str0]], m18, md8, m19, m20, entries2]

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[entries0[str0]], m18, md8, m19, m20, entries2