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Proof step 493 from proof inv-rename-file-dentry (previous step)

(key.ino = m3 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries);dirs0[key.ino]) = mkdir(m2, md, m5, m6, entries0), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, key ∈ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.dentry? ∧ key.name = dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∈ entries0 ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino = entries0[dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name] ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].dentry?

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 494:
⊦ 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 495:
(key.ino = m3 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries);dirs0[key.ino]) = mkdir(m2, md, m5, m6, entries0), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), ∀ key. key ∈ dcache0 → key.dentry? ∧ key.name = dcache0[key].name ∧ valid-dentry(key.ino, dcache0[key], dirs0, files), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.dentry? ∧ key.name = dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∈ entries0 ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].ino = entries0[dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name] ∧ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][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] → [dcache0, dirs0, files] flags: <all paths>

Additional information

Used terms: dcache0, dirs0, files