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Proof step 166 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]) = mkdir(m, md, m4, m5, entries), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ dcache, str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ ((entries0[str] = key.ino ⊃ links(key.ino, dirs0) -- mklink(m0, str);links(key.ino, dirs0)) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 167:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 168:
# links(entries0[str], dirs0) = m2 + 1, (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]) = mkdir(m, md, m4, m5, entries), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ dcache, asynced1 → synced(files0, icache0, pcache), ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs0, files0), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ ((entries0[str] = key.ino ⊃ links(key.ino, dirs0) -- mklink(m0, str);links(key.ino, dirs0)) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name] ∧ dcache[key].dentry?

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache, dirs0, files0] flags: <all paths>

Additional information

Used terms: dcache, dirs0, files0