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Proof step 28 from proof inv-renam (previous step)

new_dent.ino = entries[new_dent.name], new_dent.ino ∈ files ↔ entries0[str] ∈ files, dirs[entries0[str]] = mkdir(m15, md7, m17, m18, entries1), dirs[m] = mkdir(m12, md5, # links(m, dirs), m14, entries), files[entries0[str]] = mkfile(m5, md3, m9, content), files[new_dent.ino] = mkfile(m10, md4, m11, content0), dirs[m4] = mkdir(m13, md6, # links(m4, dirs), m16, entries0), dirs[new_dent.ino] = mkdir(m19, md8, m20, m21, entries2), new_child_inode = mkinode(new_dent.ino, md0, boolvar, m1, m2, m3), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m14, m12), old_child_inode = mkinode(entries0[str], md2, boolvar0, m6, m7, m8), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m4, md1, true, # links(m4, dirs), m16, m13), new_dent.dentry?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), new_dent.name ∈ entries, m4 ∈ dirs, str ∈ entries0, m ∈ dirs, new_dent.ino ∈ dirs → new_dent.ino ≠ ROOT_INO ∧ entries2 = ∅, asynced → synced(files, icache, pcache), m = m4 → md = md1, new_dent.ino ∈ dirs ∧ m1 = m20 ∧ m3 = m19 ∧ m2 = m21 ∧ boolvar ∨ entries0[str] ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar, new_dent.ino ∈ dirs ∨ entries0[str] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO, entries0[str] ∈ dirs ∨ entries0[str] ∈ files, entries0[str] ∈ dirs ∧ m6 = m17 ∧ m8 = m15 ∧ m7 = m18 ∧ boolvar0 ∨ entries0[str] ∈ files ∧ m6 = m9 ∧ m7 = 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) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
m0 ∈ files ↔ entries0[str] ∈ files, dirs[m0] = mkdir(m19, md8, m20, m21, entries2), dirs[m4] = mkdir(m13, md6, # links(m4, dirs), m16, entries0), files[m0] = mkfile(m10, md4, m11, content0), files[entries0[str]] = mkfile(m5, md3, m9, content), dirs[m] = mkdir(m12, md5, # links(m, dirs), m14, entries), dirs[entries0[str]] = mkdir(m15, md7, m17, m18, entries1), m0 = entries[str0], new_child_inode = mkinode(m0, md0, boolvar, m1, m2, m3), new_dent = mkdentry(str0, m0), new_parent_inode = mkinode(m, md, true, # links(m, dirs), m14, m12), old_child_inode = mkinode(entries0[str], md2, boolvar0, m6, m7, m8), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m4, md1, true, # links(m4, dirs), m16, m13), new_dent.dentry?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, str ∈ entries0, m4 ∈ dirs, str0 ∈ entries, m = m4 → md = md1, asynced → synced(files, icache, pcache), m0 ∈ dirs → m0 ≠ ROOT_INO ∧ entries2 = ∅, entries0[str] ∈ dirs ∧ m6 = m17 ∧ m8 = m15 ∧ m7 = m18 ∧ boolvar0 ∨ entries0[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0, entries0[str] ∈ dirs ∨ entries0[str] ∈ files, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, m0 ∈ dirs ∨ entries0[str] ∈ files, m0 ∈ dirs ∧ m1 = m20 ∧ m3 = m19 ∧ m2 = m21 ∧ boolvar ∨ entries0[str] ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar ⊦ ⟪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) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [new_dent, str0, m0]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: new_dent, str0, m0