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Proof step 13 from proof inv-rename-dentry (previous step)

old_child_inode.ino = dirs[m0].entries[str0], dirs[m].entries[str] ∈ files ↔ old_child_inode.ino ∈ files, new_child_inode = mkinode(dirs[m].entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_dent = mkdentry(str0, old_child_inode.ino), old_parent_inode = mkinode(m0, md0, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, m ∈ dirs, m0 ∈ dirs, dirs[m].entries[str] ∈ dirs → dirs[m].entries[str] ≠ ROOT_INO ∧ dirs[dirs[m].entries[str]].entries = ∅, m = m0 → md = md0, asynced → synced(files, icache, pcache), dirs[m].entries[str] ∈ dirs ∨ old_child_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, old_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, dirs[m].entries[str] ∈ dirs ∧ m2 = dirs[dirs[m].entries[str]].nlink ∧ m4 = dirs[dirs[m].entries[str]].size ∧ m3 = dirs[dirs[m].entries[str]].nsubdirs ∧ boolvar ∨ old_child_inode.ino ∈ files ∧ m2 = files[dirs[m].entries[str]].nlink ∧ m3 = 0 ∧ ¬ boolvar, old_child_inode.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_child_inode.ino].nlink ∧ old_child_inode.size = dirs[old_child_inode.ino].size ∧ old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs ∧ old_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ old_child_inode.nlink = files[old_child_inode.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory ⊦ ⟪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 14:
dirs[m].entries[str] ∈ files ↔ m1 ∈ files, m1 = dirs[m0].entries[str0], new_child_inode = mkinode(dirs[m].entries[str], md1, boolvar, m2, m3, m4), new_dent = mkdentry(str, dirs[m].entries[str]), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(m1, md2, boolvar0, m5, m6, m7), old_dent = mkdentry(str0, m1), old_parent_inode = mkinode(m0, md0, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), 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 ∈ dirs[m0].entries, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), m = m0 → md = md0, dirs[m].entries[str] ∈ dirs → dirs[m].entries[str] ≠ ROOT_INO ∧ dirs[dirs[m].entries[str]].entries = ∅, m1 ∈ dirs ∧ m5 = dirs[m1].nlink ∧ m7 = dirs[m1].size ∧ m6 = dirs[m1].nsubdirs ∧ boolvar0 ∨ m1 ∈ files ∧ m5 = files[m1].nlink ∧ m6 = 0 ∧ ¬ boolvar0, dirs[m].entries[str] ∈ dirs ∧ m2 = dirs[dirs[m].entries[str]].nlink ∧ m4 = dirs[dirs[m].entries[str]].size ∧ m3 = dirs[dirs[m].entries[str]].nsubdirs ∧ boolvar ∨ m1 ∈ files ∧ m2 = files[dirs[m].entries[str]].nlink ∧ m3 = 0 ∧ ¬ boolvar, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, m1 ∈ dirs ∨ m1 ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, dirs[m].entries[str] ∈ dirs ∨ m1 ∈ 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)))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [old_child_inode, m1, md2, boolvar0, m5, m6, m7]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: old_child_inode, m1, md2, boolvar0, m5, m6, m7